Congruency of shapes

These are the things you should know for proving shapes(mostly triangles) are congruent.

congruent triangles

2 triangles are congruent if and only if all pairs of corresponding sides and angles are congruent

congruent polygons

two polygons whose corresponding sides and angles are congruent when you name you must name corresponding verticals in order

Third Angles Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Side-Side-Side (SSS)

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Angle-Side-Angle (ASA)

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

AAS Theorem

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

isosoles triangle

has at least two congruent sides and two congruent angles

Converse of the Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Theorem 4-5 - Perpendicular Bisector Equidistant Theorem - PBET

If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base

vertex

A point where two or more straight lines meet.

collorary

Therom that proves a theorom

Corollary to Theorem 4-3

If a triangle is equilateral, then the triangle is equiangular

Corollary to theorem 4-4

If a triangle is equiangular, then the triangle is equilateral.

Hypotenuse Leg Theorem

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Conditions for HL theorem

1. There are two right triangles
2. The triangles have congruent hypotenuses
3. There is one pair of congruent legs

Hypotenuse

the side of a right triangle opposite the right angle