Honors Geometry Companion Book, Volume 1

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. _____ ? Reex. Prop. of ≌ b. _____ ? c. _____ ?

P

S

d. _____ ? QPS ≌ △ SRQ

a. _____ ? Reex. 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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