Question

Copy the problem, mark the givens in the diagram, and write a Statement/Reason proof. Given: CS ≅ HR ∠CHS ≅ ∠HCR ∠CSH ≅ ∠HRC Prove: CR ≅ HS

Answer 1

Answer:

Step-by-step explanation:

Given:      CS ≅ HR

           ∠CHS ≅ ∠HCR

           ∠CSH ≅ ∠HRC

Prove: CR ≅ HS

ΔCHS ≅ ΔHCR (Angle-Angle-Side, AAS, congruence property)

ΔICR ≅ ΔIHS (congruence property)

IS ≅ IR (similarity property)

CS ≅ HR (given)

Thus,

IC = IS + SC (addition property)

IH = IR + RH (addition property)

IC ≅ IH

Then,

CR ≅ HS (similarity property of triangles SCH and RHC)