Geometry

HS Mathematics

Unit: 04 Lesson: 02

Proving Triangles Congruent and CPCTC - NOTES

The definition of congruent triangles states two triangles are congruent if and only if their corresponding parts are congruent. If and only if is used when both the conditional and its converse are true. Therefore the converse is true:

Corresponding parts of congruent triangles are congruent. (CPCTC)

This can be used to prove parts of triangles congruent by first proving the triangles congruent.

Examples: Justify the following using two column or flow proofs.

1. Prove: 2. Prove:

Teacher Notes:

1.  Show triangles congruent by SSS and by CPCTC.

2.  Show triangles congruent by AAS or HA and by CPCTC.


Proving Triangles Congruent and CPCTC - HOMEWORK

Practice Problems

1. Given: is an isosceles triangle with vertex M.

bisects .

Prove:

Statements / Reasons
is an isosceles triangle with vertex M. bisects .

2. Given: ,

Prove:

Statements / Reasons
,
and are right angles.


Proving Triangles Congruent and CPCTC

3. Given: C is the midpoint

of

Prove:

Statements / Reasons
C is the midpoint of

4. Given: ,

Prove:

Statements / Reasons
,

©2012, TESCCC 07/23/12 page 2 of 3