Triangle ABC is similar to triangle PQR, as shown below: Two similar triangles ABC and PQR are shown. Triangle ABC has sides AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r, QR = p, and PR = q. Angle CAB is congruent to angle RPQ. Angle ABC is congruent to angle RQP. Angle ACB is congruent to angle QRP. Which ratio is equal to r:c? c:p p:a r:a q:c

Accepted Solution

Answer:p:aStep-by-step explanation:given: AB=c, BC=a, CA=b           PQ=r, QP=p, PR=q   also , ∠CAB ≅ ∠RPQ,--------- (1)           , ∠ABC ≅ ∠RQP,---------(2)     and, ∠ACB ≅ ∠QRP,---------(3)FROM (1), (2) AND (3),we can say that a=p, b=q, c=rtherefore, the triangles are congruent (S.S.S congruence criteria),also then, r:c=1then the ratio equal to r:c, will be p:a ( since p=a and p:a would be =1)