Download Student Notes 4.4 Proving triangles congruent SSS, SAS

4.4
Proving Triangles Congruent: SSS, SAS
When 2 triangles are congruent, __________________ angles and
_____________________ sides are congruent.
However, we do not need all 6 parts to prove triangle congruency.
SSS Postulate
If 3 ___________ of one triangle are congruent to 3 _____________ of another triangle then the triangles are
__________________.
Ex.
Given:
TS ≅ PQ
P
T
SR ≅ QR
RT ≅ RP
Q
R
S
Then
∆ _____ ≅ ∆ ______
by _______
SAS Postulate
If 2 ________ and the ________________ _________ of one triangle are congruent to 2 _________ and the
__________________ __________ of another triangle then the triangles are _______________.
Ex.
<𝑄 ≅<𝑋
𝑃𝑄 ≅ 𝑊𝑋 𝑆𝑄 ≅ 𝑌𝑋
Q
P
So ∆ _______ ≅ ∆ ________ by ________
S
X
W
Y
Example 1:
𝐴𝐸 ≅ 𝐶𝐸
𝐵𝐸 ≅ 𝐷𝐸
B
C
< 1 ≅< 2
E
1
So ∆ ________ ≅ ∆ _________
by
2
________
A
Example 2:
Given: 𝑄𝑃 ≅ 𝑆𝑃 𝑄𝑅 ≅ 𝑆𝑅
D
Q
S
P
Can you prove any triangles congruent? If so explain.
R
What is the included angle between QR and PR?
Example 3:
Can you prove any triangles congruent? If so explain.
A
𝐴𝐵 ≅ 𝐴𝐷
< 𝐷𝐴𝐶 ≅< 𝐵𝐴𝐶
D
Example 4:
Given:
DR ⊥ AG
B
C
D
RA ≅ RG
Prove: ∆ 𝐷𝑅𝐴 ≅ ∆ 𝐷𝑅𝐺
A
Homework: TB p 270 16-19 all, 27, 28, 30, 31, 35, 38-40 all
R
G