Question

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

Answer 1

Answer:

p:a

Step-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=r

therefore, the triangles are congruent (S.S.S congruence criteria),

also then, r:c=1

then the ratio equal to r:c, will be p:a ( since p=a and p:a would be =1)