Download 4.3 Using Congruent Triangles

Geometry
4.3 Using Congruent Triangles
In yesterday’s lesson you learned how
to prove two triangles congruent by
SSS
SAS
ASA
After 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
Plan the Proof:

Prove: Q

7
Plan:
1

Δ PQR

1
2
S


R
S
2
PS
PR
Δ PSR by SAS, so
7
7
PR
P
Q

7
7
PQ
QPS
PS
7
PQ
7
Given: PR bisects
Q
S (CPCTC)
Plan the Proof:
ZW

Prove: WX
WX
ZW
ZX
Δ ZWX

so WX
Y
3
XY
ZY
W
 YZ


ZX

ZY because Alt Int. <‘s 
1
4
X
XY
Δ XYZ by SSS, so
2
1
7
Plan:
Z
 YZ
7
Given: WX
2 (CPCTC),
lines
Lines
to a Plane
A
Given:
M is the midpoint of AB
plane X
AB at M
X
M
What can you deduce about AP and BP ?
Plan:
Δ APM
so AP


Δ BPM by SAS
BP (CPCTC)
B
P
Let’s try a few from the HW
Please open your books to page 130 #2
and #4
Homework
pg. 130 # 1 - 8