Exploring Congruent Triangles

Congruent triangles: Triangles that are the same size and shape – Each triangle has six parts, three angles and three sides – If the corresponding six parts of one triangle are congruent to the six parts of another triangle, then the triangles are congruent This is abbreviated by CPCTC (corresponding parts of congruent triangles are congruent) – Orientation of the triangles is not important. This means that the triangles can be flipped, slid and turned around, and if the corresponding parts are congruent, the triangles are congruent

Segments: Angles: Note: The order matters. If  ABC   DEF, it is not the same as saying  ABC   FED.

EXAMPLE 1: If  ABC   RQC, name the corresponding congruent sides and angles. Congruent Sides – Congruent Angles –

Write the correct congruency statement. Compare the sides and the angles. Example 2

3.54.

Do worksheet Parts of congruent triangles and exploring congruent triangles.

Congruence of triangles is: Reflexive:  ABC   ABC

Congruence of triangles is: Symmetric If  ABC   DEF, then  DEF   ABC

Congruence of triangles is: Transitive If  ABC   DEF and  DEF   LMN, then  ABC   LMN.

Proving Triangle Congruency

There are 4 ways to prove that two triangles are congruent to each other. Remember, once you know that two triangles are congruent, then Corresponding Parts of Congruent Triangles are Congruent.

Side-Side-Side Postulate (SSS): If all 3 sides of one triangle are congruent to all 3 sides of another triangle, then the two triangles are congruent.

Side-Angle-Side Postulate (SAS): If two sides & the included angle (the angle between the two sides) of one triangle are congruent to two sides & the included angle of another triangle, then the two triangles are congruent. Ex:

Do worksheet ways to prove triangle congruence SAS SSS

Angle-Side-Angle Postulate (ASA): If 2 angles & the side between them in one triangle are congruent to 2 angles & the side between them in another triangle, then the 2 triangles are congruent.

Angle-Angle-Side Postulate (AAS): If 2 angles & a side not between them in one triangle are congruent to 2 angles & the corresponding side not between them in another triangle, then the 2 triangles are congruent.

Determine which Postulate or theorem can be used to prove the 2 triangles are congruent. If it’s not possible, write Not Possible. Remember, you can choose from SSS, SAS, ASA, or AAS.

Hypotenuse-Leg (HL) If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangle are congruent.

Proofs: Given : & G is the midpoint of Prove: if StatementsReasons 1) Is the midpoint of 2) 3)

Given: Prove: StatementReasons 1) 2) 3) 4)

StatementReason 1. L is the Midpoint of ΔWRL ΔEDL Given: L is the Midpoint of Prove: ΔWRL ΔEDL

StatementReason Given: Prove:

StatementReason Is a right angle Is a right angle Given: Prove: