Geometry Practice Test 4

In ΔABC and ΔPBQ,
∠B = ∠B Common
∠BCA = ∠BQP {corresponding angles}
∠BAC = ∠BPQ {corresponding angles}
∴ ΔABC ≅ ΔPBQ {by Rule AAA}
In ΔCPQ and ΔPQR,
∠Q = ∠R = 90°
PQ = PQ Common
∠P = ∠P
⇒ ΔCPQ ≅ ΔPQR by Rule {ASA}
And ΔCRQ and ΔCQP
∠R = ∠Q = 90°
∠Q = ∠Q = common.
∠C = ∠C = common
⇒ ΔCRQ ≅ ΔCQP {by Rule {ASA}}