Transcript Geometry
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
YZ
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
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 BPM by SAS
so AP BP (CPCTC)
Δ APM
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