4.2.2 Triangle Congruence: ASA, AAS, and HL - Worksheet
Example 1 & 2: Determine if you can use ASA to prove the triangles congruent. Explain. 1. △ VRS and △ VTS, given that VS bisects ∠ RST and ∠ RVT 2. △ DEH and △ FGH
D
E
T
H
S
V
F
G
R
Example 3: 3. Use AAS to prove the triangles congruent. Given: ∠ R and ∠ P are right angles. QR || SP Prove: △ QPS ≅ △ SRQ Proof:
Q
R
Proof:
QR || PS Given ∠ R ≌ ∠ P Alt. Int. ∠ s Thm. △ a. _____ ? Re ex. Prop. of ≌ b. _____ ? c. _____ ?
P
S
d. _____ ? QPS ≌ △ SRQ
a. _____ ? Re ex. Prop. of ≌ b. _____ ? ∠ R ≌ ∠ P Alt. Int. ∠ Thm. � c. _____ ?
QR || PS Given
d. ____ ? QPS ≌ � S
∠ R and ∠ P are rt. ∠ s .
Given
∠ R and ∠ P are rt. ∠ .
Given
Example 4: Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know. 4. △ ABC and △ CDA A D 5. △ XYV and △ ZYV V
B
C
X
Z
Y
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