Geometry

4.3 Using Congruent Triangles

In yesterday’s lesson you learned how to prove two triangles congruent by

SSSSASASAAfter we prove Δ’s …….today

we will prove segments or angles using CPCTC

If 2 triangles are congruent

All of their 6 corresponding parts are congruent

A Way to Prove Two Segments or Two Angles Congruent

1. Identify 2 triangles in which the 2 segments or angles are corresponding parts

2. Prove that the 2 triangles are congruent (use SSS, ASA, or SAS)

3. State that the 2 parts are congruent, using the reason CPCTC

Given: PR bisects QPS

PQ PS

Prove: Q S

Plan the Proof:

P

Q

R

S

ΔPQR PSR by SAS, so Q S (CPCTC)

12

7

7 7Plan:

7

1 2

7

PQ PS

PQ PS

PR PR

Δ 7 7

Given: WX YZ

ZW XY

Prove: WX ZY

Plan the Proof:

ΔZWX XYZ by SSS, so 1 2 (CPCTC),

so WX ZY because Alt Int. <‘s lines

Plan:

Δ 7 7

14

32

Z

W

Y

X

WX YZ

ZW XY

ZX ZX

Plan: Δ APM Δ BPM by SAS

so AP BP (CPCTC)

Lines to a Plane

MP

B

A

X

Given: M is the midpoint of AB

plane X AB at M

What can you deduce about AP and BP ?

Let’s try a few from the HW

Please open your books to page 130 #2 and #4

Homework

pg. 130 # 1 - 8