G10 Triangle Congruence SSS SAS ASA AAS HL

G-10 Triangle Congruence SSS, SAS, ASA, AAS, HL I can test to see if two triangles are congruent by identifying, comparing and contrasting what it means to be ASA, SAS, SSS, AAS and HL

Don’t Write This! • In G-09, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent. • The property of triangle rigidity gives you a shortcut for proving two triangles congruent.

SSS – side, side

An included angle is an angle formed by two adjacent sides of a polygon. B is the included angle between sides AB and BC.

SAS – side, angle, side

Caution The letters SAS are written in that order because the congruent angles must be between pairs of congruent corresponding sides.

An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

ASA – angle, side, angle

AAS – angle, side

HL – Hypotenuse, leg

Example 1 a

Example 1 b

Example 1 c

Example 1 d

Example 1 e

Example 1 f

Example 1 g

Example 1 h

Example 1 i

Example 1 j

Example 2 a Determine what single piece of missing information is needed in order to show the triangles are congruent using the given postulate. SAS

Example 2 b Determine what single piece of missing information is needed in order to show the triangles are congruent using the given postulate. SAS

Example 2 c Determine what single piece of missing information is needed in order to show the triangles are congruent using the given postulate. ASA

Example 2 d Determine what single piece of missing information is needed in order to show the triangles are congruent using the given postulate. SSS

Example 2 e Determine what single piece of missing information is needed in order to show the triangles are congruent using the given postulate. ASA

Example 2 f Determine what single piece of missing information is needed in order to show the triangles are congruent using the given postulate. AAS

Example 2 g Determine what single piece of missing information is needed in order to show the triangles are congruent using the given postulate. HL

Example 3 a Given: AB CD, BC AD Prove: ΔABC ΔCDA Statement AB CD, BC AD AC ΔABC ΔCDA Reason Given

Example 3 b Given: AB CB, D is the midpt. of AC Prove: ΔABD ΔCBD Statement Reason AB CB Given D is the midpt. of AC Given AD DC BD ΔABD ΔCBD

Example 3 c Given: JL bisects KLM, K M Prove: JKL JML Statement JL bisects KLM KLJ MLJ K M JKL JML Reason Given Reflexive

Example 3 d Given: BF BC, A D Prove: ABF DBC Statement BF BC, A D Reason Given AAS

Example 3 e Given: B is the midpt. of AE and CD Prove: ABD EBC Statement Reason B is the midpt. of AE and CD Given AB BE, DB BC SAS