Unit 5 Test: Congruent Triangles

SSS

Three sides of one triangle are congruent to three sides of another triangle.

SAS

Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

ASA

Two angles and the included side of one triangle are congruent to two triangles and the included side of another triangle.

AAS

Two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle.

(R) HL

The hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle.

Third Angles Theorem

If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent

Congruent figures

*figures that have the same shape and size
*have ALL corresponding sides and angles congruent

Corresponding

geometric parts that are in the same position in different figures

Included side

A side that is between two angles in a triangle
In the figure, LM is the included side between angle L and angle M.

Included angle

An angle that is between two sides in a triangle
In the figure, angle N is the included angle between LN and MN.

Angle-Angle-Angle (AAA)

does NOT prove triangles congruent because the sides could be different lengths.

Side-Side-Angle (SSA)

does NOT prove triangles congruent because the second side acts as a hinge.

Congruent Triangles

3 pairs of corresponding angles are congruent and 3 pairs of corresponding sides are congruent.

Vertical Angles

Two angles formed by intersecting lines and facing in the opposite direction

Vertical Angles Thm.

vertical angles are congruent

Congruent transformation

performing 1 or more transformations (translations, reflection, rotation) to map one figure onto another.

congruence statement

states that two figures are congruent (ALWAYS LIST CORRESPONDING VERTICES IN THE SAME ORDER)

reflexive property

if two figures share a side/angle, then those sides/angles are congruent.

hypotenuse

the side of a right triangle opposite the right angle

leg(s) of a right triangle

Either of the two sides that form the right angle in a right triangle.

Isosceles triangle

A triangle with at least two congruent sides

Isosceles triangle thm.

If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent.

Converse of the Isosceles triangle thm.

If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent

Equilateral triangle

A triangle with three congruent sides

definition of segment bisector

a line, ray, or segment that divides a segment into two congruent segments

definition of midpoint

the point that divides a segment into 2 congruent angles

definition of angle bisector

ray that divides an angle into 2 congruent angles

definition of perpendicular

two lines that intersect to form right angles

CPCTC

*corresponding parts of congruent triangles are congruent
*If triangles are congruent, then their parts are also congruent.