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Geometrical theorem relating the lengths of two segments that divide a triangle
is the angle bisector of angle ∠ A. The generalized angle bisector theorem (which is not necessarily an angle bisector theorem, since the angle ∠ A is
Angle_bisector_theorem
Division of something into two equal or congruent parts
three-dimensional space, bisection is usually done by a bisecting plane, also called the bisector. The perpendicular bisector of a line segment is a line which meets
Bisection
Angle formed in the interior of a circle
Note that this theorem is not to be confused with the angle bisector theorem, which also involves angle bisection (but of an angle of a triangle not
Inscribed_angle
Several sets of circles associated with Apollonius of Perga
extended line AP. Again by the converse of the angle bisector theorem, the line PD bisects the exterior angle ∠QPB. Hence, γ = ∠ BPD and δ = ∠ QPD are equal
Circles_of_Apollonius
Theorem that any three objects in space can be simultaneously bisected by a plane
intermediate value theorem, there must be an angle in which p ( α ) = 1 / 2 {\displaystyle p(\alpha )=1/2} . Cutting at that angle bisects both pancakes simultaneously
Ham_sandwich_theorem
Every triangle with two angle bisectors of equal lengths is isosceles
Jakob Steiner. It states: Every triangle with two angle bisectors of equal lengths is isosceles. The theorem was first mentioned in 1840 in a letter by C.
Steiner–Lehmus_theorem
Simple curve of Euclidean geometry
ratio and lying on segment AB. By the angle bisector theorem the line segment PC will bisect the interior angle APB, since the segments are similar: A
Circle
Triangle with at least two sides congruent
the base, the angle bisector from the apex to the base, the median from the apex to the midpoint of the base, the perpendicular bisector of the base within
Isosceles_triangle
Center of the inscribed circle of a triangle
{AC}}:{\overline {AF}}={\overline {CI}}:{\overline {IF}}} , by the angle bisector theorem. In △ B C F {\displaystyle \triangle {BCF}} , B C ¯ : B F ¯ = C
Incenter
Theorem about inscribed and circumscribed circles
let D be the point where line BI (the angle bisector of ∠ABC) crosses the circumcircle of ABC. Then, the theorem states that D is equidistant from A, C
Incenter–excenter_lemma
Relation between sides of a right triangle
(the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation
Pythagorean_theorem
Mathematical model of the physical space
Type theory Angle bisector theorem Butterfly theorem Ceva's theorem Heron's formula Menelaus' theorem Nine-point circle Pythagorean theorem Eves 1963,
Euclidean_geometry
Relates the length of a median of a triangle to the lengths of its sides
parallelogram bisect each other, the theorem is equivalent to the parallelogram law. The theorem can be proved as a special case of Stewart's theorem, or can
Apollonius's_theorem
Plane curve
Q} on w . {\displaystyle w.} By the triangle inequality and the angle bisector theorem, 2 a = | L F 2 | < {\displaystyle 2a=\left|LF_{2}\right|<{}} | Q
Ellipse
On triangles inscribed in a circle with a diameter as an edge
Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's
Thales's_theorem
Ancient Greek mathematician (fl. 300 BC)
the later tradition of Alexandria. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections
Euclid
Figure formed by two rays meeting at a common point
angle bisector with the opposite extended side, are collinear. In a triangle, three intersection points, two between an interior angle bisector and the
Angle
Generalization of Pythagorean theorem
or cosine rule or Al-Kashi’s theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides a
Law_of_cosines
Angle bisector theorem (Euclidean geometry) Anne's theorem (geometry) Apollonius's theorem (plane geometry) Barbier's theorem (geometry) Beck's theorem (incidence
List_of_theorems
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It
Ancient_Greek_mathematics
Movement with a fixed point is rotation
out that O can be found by intersecting the perpendicular bisector of Aa with the angle bisector of ∠αAa, a construction that might be easier in practice
Euler's_rotation_theorem
Problem of constructing equal-area shapes
proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi ( π {\displaystyle \pi } ) is a transcendental number
Squaring_the_circle
Shape with three sides
acute. An angle bisector of a triangle is a straight line through a vertex that cuts the corresponding angle in half. The three angle bisectors intersect
Triangle
Statement on the gravitational attraction of spherical bodies
and HK such that the angle KPL is very small. JM is the line through P that bisects that angle. From the inscribed angle theorem, the triangles IPH and
Shell_theorem
Line intersecting both a vertex and opposite edge of a triangle
angle bisectors, altitudes are all special cases of cevians. The name cevian comes from the Italian mathematician Giovanni Ceva, who proved a theorem
Cevian
Property of objects which are scaled or mirrored versions of each other
this way are: the angle bisector theorem, the geometric mean theorem, Ceva's theorem, Menelaus's theorem and the Pythagorean theorem. Similar triangles
Similarity_(geometry)
Theorem on cyclic quadrilateral
similarly: the angles FDM, BCM, BME and DMF are all equal, so DFM is an isosceles triangle, so FD = FM. It follows that AF = FD, as the theorem claims. Brahmagupta's
Brahmagupta_theorem
Exterior angle of a triangle is greater than either of the remote interior angles
The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either
Exterior_angle_theorem
Triangle containing a 90-degree angle
opposite the right angle), and a {\displaystyle a} and b {\displaystyle b} are the lengths of the legs (remaining two sides). This theorem was proven in antiquity
Right_triangle
Geometric theorem involving midpoints on a triangle
theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect
Midpoint_theorem_(triangle)
Relates the 4 sides and 2 diagonals of a quadrilateral with vertices on a common circle
demonstration of Ptolemy's theorem, based on Derrick & Herstein (2012). Let ABCD be a cyclic quadrilateral. On the chord BC, the inscribed angles ∠BAC = ∠BDC, and
Ptolemy's_theorem
Problem-solving technique in geometry
the angle bisector theorem. Stewart's theorem - When asked not for the ratios of lengths but for the actual lengths themselves, Stewart's theorem may
Mass_point_geometry
Theorem in geometry
Perpendicular bisector construction of a quadrilateral, a different way of forming another quadrilateral from a given quadrilateral Morley's trisector theorem, a
Varignon's_theorem
Geometry without using coordinates
Butterfly theorem, Angle bisector theorem, Apollonius' theorem, British flag theorem, Ceva's theorem, Equal incircles theorem, Geometric mean theorem, Heron's
Synthetic_geometry
Quadrilateral with two pairs of parallel sides
opposite angles are equal in measure. The diagonals bisect each other. One pair of opposite sides is parallel and equal in length. Adjacent angles are supplementary
Parallelogram
Circles tangent to all three sides of a triangle
intersection of the three internal angle bisectors. The center of an excircle is the intersection of the internal bisector of one angle (at vertex A, for example)
Incircle_and_excircles
Characterizes spherical triangles with fixed base and area
the perpendicular bisector of the base, and the triangle of maximal area has its apex at the far intersection. However, this theorem is also a straightforward
Lexell's_theorem
Convex quadrilateral with at least one pair of parallel sides
{\displaystyle {\frac {a+2b}{2a+b}}.} If the angle bisectors to angles A and B intersect at P, and the angle bisectors to angles C and D intersect at Q, then P Q
Trapezoid
Elements Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Hinge theorem Inscribed angle theorem Intercept
A History of Greek Mathematics
A_History_of_Greek_Mathematics
Equality of areas of a sliced disk
that a pizza sliced in the same way as the pizza theorem, into a number n of sectors with equal angles where n is divisible by four, can also be shared
Pizza_theorem
Geometric theorem about isosceles triangles
In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ˈpɒnz
Pons_asinorum
Construction of an angle equal to one third a given angle
into an arbitrary set of equal segments, to draw parallel lines, to bisect angles, to construct many polygons, and to construct squares of equal or twice
Angle_trisection
Points on a common circle
O must lie on the perpendicular bisector of the line segment PQ. For n distinct points there are n(n − 1)/2 bisectors, and the concyclic condition is
Concyclic_points
Altitude (triangle) Area bisector of a triangle Angle bisector of a triangle Angle bisector theorem Apollonius point Apollonius' theorem Automedian triangle
List_of_triangle_topics
On tangency patterns of circles
for both graphs that cross at right angles. Circle packings and their tangencies, and the circle packing theorem, have been extended to arbitrary Riemannian
Circle_packing_theorem
Existence of geodesic circles on surfaces
In differential geometry the theorem of the three geodesics, also known as Lyusternik–Schnirelmann theorem, states that every Riemannian manifold with
Theorem of the three geodesics
Theorem_of_the_three_geodesics
Line joining midpoints of a complete quadrilateral's 3 diagonals
of ∠BEC, that is, each line is a reflection of the other about the angle bisector. (Figure 2) Triangles △EDF, △NPM are similar by the above argument,
Newton–Gauss_line
In a quadrilateral with all sides tangent to a circle, sums of opposite sides are equal
to prove the converse of the theorem is to use three sides to construct the circle. Namely, construct the angle bisectors at B and C and let them intersect
Pitot_theorem
Perpendicular line segment from a triangle's side to opposite vertex
altitude having the incongruent side as its base will be the angle bisector of the vertex angle. In a right triangle, the altitude drawn to the hypotenuse
Altitude_(triangle)
colored with two colors. Kawasaki's theorem or Kawasaki-Justin theorem: at any vertex, the sum of all the odd angles (see image) adds up to 180 degrees
Mathematics_of_paper_folding
Plane curve: conic section
theorems that can be deduced simply from the above argument. The above proof and the accompanying diagram show that the tangent BE bisects the angle ∠FEC
Parabola
Universality of construction using just a straightedge and a single circle with center
In Euclidean geometry, the Poncelet–Steiner theorem is a result about compass and straightedge constructions with certain restrictions. This result states
Poncelet–Steiner_theorem
Part of a circle between two points
perpendicular bisector is another chord, which is a diameter of the circle. The length of the first chord is W, and it is divided by the bisector into two
Circular_arc
Relationship between two lines that meet at a right angle
the SSS congruence theorem for QPA' and QPB' to conclude that angles OPA' and OPB' are equal. Then use the SAS congruence theorem for triangles OPA' and
Perpendicular
know what AA postulate can be used for. It is used proving the Angle Bisector Theorem. AA postulate is one of the many similarity ways for determining
AA_postulate
Ancient Greek mathematician
Elements Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Hinge theorem Inscribed angle theorem Intercept
Leon_(mathematician)
Quadrilateral whose vertices lie on a circle
direct theorem was Proposition 22 in Book 3 of Euclid's Elements. Equivalently, a convex quadrilateral is cyclic if and only if each exterior angle is equal
Cyclic_quadrilateral
Shape with three equal sides
equilateral triangle are all equal in length, resulting in the median and angle bisector being equal in length, considering those lines as their altitude depending
Equilateral_triangle
Ancient Greek spherical geometry treatise
astronomy as modeled by the celestial sphere. Primarily consisting of theorems which were known at least informally a couple centuries earlier, the Spherics
Theodosius'_Spherics
Problem of finding unknown lengths and angles of a triangle
the included angle (SAS, side-angle-side) Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than
Solution_of_triangles
Four-sided polygon
rhombus. Rectangle: all four angles are right angles (equiangular). An equivalent condition is that the diagonals bisect each other, and are equal in
Quadrilateral
Triangle with integer side lengths
the angle bisector w a {\displaystyle w_{a}} of the angle α {\displaystyle \alpha } , the angle bisector w b {\displaystyle w_{b}} of the angle β {\displaystyle
Integer_triangle
Quadrilateral with four right angles
perpendicular bisector of those sides, but, in the case of the crossed rectangle, the first axis is not an axis of symmetry for either side that it bisects. Quadrilaterals
Rectangle
Method of drawing geometric objects
perpendicular bisector from a segment Finding the midpoint of a segment. Drawing a perpendicular line from a point to a line. Bisecting an angle Mirroring
Straightedge and compass construction
Straightedge_and_compass_construction
Number, approximately 1.618
is made by the angle bisector, because it is the only isosceles triangle whose base angle is twice its apex angle. The angle bisector of the golden triangle
Golden_ratio
Trapezoid symmetrical about an axis
length. The base angles of an isosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is the supplementary
Isosceles_trapezoid
perpendicular with a right angle between them, is half of a rectangle with the two perpendicular sides as its base and height, bisected along a diagonal. Thus
Area_of_a_triangle
Condition for 3 lines with common point to be perpendicular to the sides of triangle
Carnot's theorem (named after Lazare Carnot) describes a necessary and sufficient condition for three lines that are perpendicular to the (extended) sides
Carnot's theorem (perpendiculars)
Carnot's_theorem_(perpendiculars)
Circle that passes through the vertices of a triangle
vertices; its radius is the circumradius. Any point on a perpendicular bisector of one side is equidistant from the two adjacent vertices of the triangle
Circumcircle
Theorem in hyperbolic geometry
They are the same distance from r and both lie on s. So the perpendicular bisector of D'D (a segment of s) is also perpendicular to r. (If r and s were asymptotically
Ultraparallel_theorem
Shape with five sides
the periphery vertically above the center at point D. Angle CMD is bisected, and the bisector intersects the vertical axis at point Q. A horizontal line
Pentagon
Convex, 4-sided shape with an incircle and a circumcircle
opposite sides satisfy Pitot's theorem for tangential quadrilaterals and the cyclic quadrilateral property that opposite angles are supplementary; that is
Bicentric_quadrilateral
Plane algebraic curve
the interior angle at O. The lemniscate is symmetric to the line connecting its foci F1 and F2 and as well to the perpendicular bisector of the line segment
Lemniscate_of_Bernoulli
Mathematical treatise by Euclid
parallelograms (35–45), and the Pythagorean theorem and its converse (46–48). Proposition 5, that the base angles of an isosceles triangle are equal, became
Euclid's_Elements
OI^{2}<OH^{2}-2\cdot IH^{2}<2\cdot OI^{2}.} The larger of two angles of a triangle has the shorter internal angle bisector: If A > B then t a < t b . {\displaystyle {\text{If}}\quad
List_of_triangle_inequalities
Geometric theorem
ABC be a triangle with side AB congruent to side AC. Draw the angle bisector of angle A and let D be the point at which it meets side BC. And so on.
Crossbar_theorem
Point on a line segment which is equidistant from both endpoints
midpoint of XY. The midpoint of any segment which is an area bisector or perimeter bisector of an ellipse is the ellipse's center. The ellipse's center
Midpoint
B'I". Then, line OA is the angle bisector for ᗉ IAI'. Case 2c: IB' is ultraparallel to I'B. Using the ultraparallel theorem, construct the common perpendicular
Constructions in hyperbolic geometry
Constructions_in_hyperbolic_geometry
2 points about which a triangle can be inverted into an equilateral triangle
for each of the three pairs of circles of Apollonius. The perpendicular bisector of line segment S S ′ {\displaystyle SS'} is the Lemoine line, which contains
Isodynamic_point
Line which touches a circle at exactly one point
an angle bisector of any pair of the lines; there are two angle-bisecting lines for every intersection of two lines. The intersections of these angle bisectors
Tangent_lines_to_circles
Polyhedron with four faces
circumcenter of a tetrahedron can be found as intersection of three bisector planes. A bisector plane is defined as the plane centered on, and orthogonal to
Tetrahedron
Circles in two perpendicular families
perpendicular bisector of CD. The hyperbolic pencil defined by points C, D (the blue circles) has its radical axis on the perpendicular bisector of line CD
Apollonian_circles
perpendicular bisector passes through the center of the circle and bisects the angle. One half of the bisected chord is the sine of one half the bisected angle, that
History_of_trigonometry
Theorem relating the number of edges, vertices and faces of a polyhedron
mathematics, and more particularly in polyhedral combinatorics, Eberhard's theorem partially characterizes the multisets of polygons that can form the faces
Eberhard's_theorem
Lines which intersect at a single point
example: Any median (which is necessarily a bisector of the triangle's area) is concurrent with two other area bisectors each of which is parallel to a side.
Concurrent_lines
Trigonometric values in terms of square roots and fractions
follows from the Pythagorean theorem, and the sine values for 36° and 54° follow from sin(18°) and the double- and triple-angle formulas. Wikimedia Commons
Exact_trigonometric_values
Plane curve: conic section
semi major axis of the hyperbola). Line w {\displaystyle w} is the bisector of the angle between the lines P F 1 ¯ , P F 2 ¯ {\displaystyle {\overline {PF_{1}}}
Hyperbola
Circle tangent to two sides of a triangle and its circumcircle
{\displaystyle {\sqrt {AB\cdot AC}}} and a reflection with respect to the angle bisector on A {\displaystyle A} . Since inversion and reflection are bijective
Mixtilinear incircles of a triangle
Mixtilinear_incircles_of_a_triangle
Convex polygon that contains an inscribed circle
convex polygon has an incircle if and only if all of its internal angle bisectors are concurrent. This common point is the incenter (the center of the
Tangential_polygon
Construct all the circles that are tangent to three given circles
through them (operation 1) is the perpendicular bisector. To generate the line that bisects the angle between two given rays[clarification needed] requires
Special cases of Apollonius' problem
Special_cases_of_Apollonius'_problem
Line segment joining a triangle's vertex to the midpoint of the opposite side
the medians not in a 2:1 ratio but in a 3:1 ratio (Commandino's theorem). Angle bisector Altitude (triangle) Automedian triangle Weisstein, Eric W. (2010)
Median_(geometry)
Line constructed from a triangle
Forum Geometricorum 13 (2013) 153–164: Theorem 4. Olga Radko and Emmanuel Tsukerman, "The Perpendicular Bisector Construction, the Isoptic point, and the
Simson_line
On smallest surface enclosing two volumes
bubble: three spherical surfaces meeting at angles of 120° on a common circle. The double bubble theorem was formulated and thought to be true in the
Double_bubble_theorem
Shape with four equal sides and angles
angle). The central angle of a square is equal to 90°. The external angle of a square is equal to 90°. The diagonals of a square are equal and bisect
Square
Spheres tangent to a plane inside a cone
intersection of the plane with the cone is symmetric about the perpendicular bisector of the line through F1 and F2 may be counterintuitive, but this argument
Dandelin_spheres
Line containing one side of a polygon
them between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended
Extended_side
Integer side lengths of a right triangle
theorem 90 Integer triangle Modular arithmetic Nonhypotenuse number Plimpton 322 Pythagorean prime Pythagorean quadruple Quadric Tangent half-angle formula
Pythagorean_triple
On sums of distances in triangles
left side cannot be smaller than the right side. Now reflect P on the angle bisector at C. We find that cr ≥ ay + bx for P's reflection. Similarly, bq ≥
Erdős–Mordell_inequality
Half of the sum of side lengths of a polygon
half-angles at the vertices of a triangle in terms of the semiperimeter, the sides, and the inradius. The length of the internal bisector of the angle opposite
Semiperimeter
Convex 4-sided polygon whose sidelines are all tangent to an outside circle
six angle bisectors. These are the internal angle bisectors at two opposite vertex angles, the external angle bisectors (supplementary angle bisectors) at
Ex-tangential_quadrilateral
ANGLE BISECTOR-THEOREM
ANGLE BISECTOR-THEOREM
Girl/Female
Christian, French, German, Greek
Angel; A Messenger from God
Female
English
English short form of Latin Angela, ANGIE means "angel, messenger."
Female
English
English short form of Latin Angela, ANGE means "angel, messenger." Compare with masculine Ange.
Boy/Male
American, British, Danish, English, French, German, Greek, Hindu, Indian, Latin, Spanish
Messenger of God; Angel; Messenger
Girl/Female
Latin American Greek
Angel; Like an angel. From angelicus meaning angelic.
Girl/Female
French
Angel.
Surname or Lastname
English
English : from Middle English angel ‘angel’ (from Latin angelus), probably applied as a nickname for someone of angelic temperament or appearance or for someone who played the part of an angel in a pageant. As a North American surname it may also be an Americanized form of a cognate European surname, as for example Italian Angelo, Rumanian Anghel, Czech Anděl, or Hungarian Angyal.German : ethnic name for a member of a Germanic people on the Jutland peninsula; members of this tribe invaded eastern and northern Britain in the 5th–6th centuries and gave their name to England. See Engel.Slovenian (eastern Slovenia) : from the Latin personal name Angelus.
Female
English
English unisex name derived from Latin Angelus, ANGEL means "angel, messenger."Â Originally a male name, it is now almost strictly female.
Girl/Female
Indian
Pari fairy
Girl/Female
American, Australian, Greek, Portuguese
Like an Angel; Befitting in Angle
Male
French
French name ANGE means "angel, messenger." Compare with feminine Ange.
Surname or Lastname
English and Irish (of Norman origin)
English and Irish (of Norman origin) : topographic name from Middle English and Old French angle ‘angle’, ‘corner’ (Latin angulus). As an Irish surname, it can also be habitational, from a place in Pembrokeshire, South Wales, named with this word.Americanized spelling of German Angel or Engel.
Male
English
English unisex name derived from Latin Angelus, ANGEL means "angel, messenger." Once used as a man's name in England. It is now almost strictly a feminine name.
Boy/Male
German, Swedish
Angel; Bright Angle
Boy/Male
Spanish American Greek Latin
Angel.
Girl/Female
English
Good Fairy
Girl/Female
Greek American Italian Latin
Messenger or angel. A popular masculine name in Sicily after the 13th-century saint, Angel. Angel...
Girl/Female
British, English, Greek, Latin
Angel
Female
Greek
(Αίγλη) Greek name AIGLE means "radiance, splendor." In mythology, this is the name of several characters, including a goddess of good health.
Boy/Male
American, Danish, French, German, Greek, Indian, Italian, Spanish
Angel
ANGLE BISECTOR-THEOREM
ANGLE BISECTOR-THEOREM
Girl/Female
Indian
A tree which yields An Aroma
Male
English
English name derived from the vocabulary word, from the Middle English word sterrling, STERLING means "little star."Â
Girl/Female
Tamil
Girl/Female
Tamil
Beloved, Goddess of Love
Girl/Female
Sikh
Praise of one
Girl/Female
Tamil
Sivasathi | ஸிவாஸதீ
Goddess Sita
Boy/Male
Celtic American English French
Strong.
Boy/Male
Egyptian
God of mystery.
Boy/Male
Hindu, Indian
Compassionate; Kind; Merciful Person
Girl/Female
Australian, German, Kurdish
Life; Loved One
ANGLE BISECTOR-THEOREM
ANGLE BISECTOR-THEOREM
ANGLE BISECTOR-THEOREM
ANGLE BISECTOR-THEOREM
ANGLE BISECTOR-THEOREM
a.
Having eight angles; eight-angled.
n.
One who, or that which, bisects; esp. (Geom.) a straight line which bisects an angle.
n.
One who angles.
a.
Relating to an angle or to angles; having an angle or angles; forming an angle or corner; sharp-cornered; pointed; as, an angular figure.
n.
A favorite; a paramour; an ingle.
a.
Containing a right angle or right angles; as, a right-angled triangle.
n.
The difference of direction of two lines. In the lines meet, the point of meeting is the vertex of the angle.
a.
Having oblique angles; as, an oblique-angled triangle.
n.
A paramour; a favourite; a sweetheart; an engle.
v. i.
To use some bait or artifice; to intrigue; to scheme; as, to angle for praise.
n.
See Ankle.
a.
Having acute angles; as, an acute-angled triangle, a triangle with every one of its angles less than a right angle.
v. t.
To cause to dangle; to swing, as something suspended loosely; as, to dangle the feet.
v. i.
To fish with an angle (fishhook), or with hook and line.
imp. & p. p.
of Angle
a.
Having an angle or angles; -- used in compounds; as, right-angled, many-angled, etc.
imp. & p. p.
of Bisect
n.
To smooth with a mangle, as damp linen or cloth.
v. t.
To cajole or coax; to wheedle. See Engle.