Honors geometry chapter 4

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Congruent figures

figures with the same size and shape

rigid motions

Slide, flip, turn a shape so that it fits another one

corresponding parts

corresponding parts of congruent figures are congruent. When all corresponding parts of two triangles are congruent then the triangles are congruent.

Reflexive properties of triangle congruence

For any triangle, triangle ABC is congruent to triangle ABC

Symmetric properties of triangle congruence

if ABC is congruent to DEF then DEF is congruent to ABC

Transitive properties of triangle congruence

if ABC is congruent to DEF and DEF is congruent to JKL the ABC is congruent to JKL

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 angle side (SAS) congruence theorem

if two sides and the included angle of one one triangle are congruent to two sides and the included angle of a second triangle then they are congruent

Base angle theorem

If two sides of a triangle are congruent then the angles opposite them are congruent

Converse of the base angles theorem

if two angles of a triangle are congruent then the sides opposite them are congruent

Corollary to the base angles theorem

If a triangle is equilateral then it is equiangular  

Corollary to the converse of the base angles theorem

if a triangle is equiangular then it is equilateral

Side side side (SSS) congruence theorem

If three sides of one triangle are congruent to three sides of a second triangle then the two triangles are congruent.

Legs

The sides adjacent to the right angle

Hypotenuse

the side opposite of the right angle

Hypotenuse leg (HL) congruence theorem

if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle then the two triangles are congruent.

Angle side angle (ASA) congruence theorem

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

Angle angle side (AAS) congruence theorem

if two angles and a non included side of a triangle are congruent to two angles and the corresponding non included side of a second triangle then the two triangles are congruent.

Coordinate proof

placing geometric figures in a coordinate plane. When you use variables to represent the coordinates of a figure in a coordinate proof, the results are true for all figures of that type.