Triangle abc is similar to triangle pqr, as shown below: which equation is correct?

Asked by maham237 @ 19/12/2020 in Mathematics viewed by 372 People

Triangle ABC has sides AB equals c, BC equals a, and AC equals b. Triangle PQR has sides PQ equals r, QR equals p, and PR equals q. Angle CAB is congruent to angle RPQ. Angle ABC is congruent to angle RQP. Angle ACB is congruent to angle QRP.

Which equation is correct?

Answered by maham237 @ 19/12/2020

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.

Since all three angles of one triangle are congruent to three angles of another triangle, then these triangles are similar by AAA theorem. Congruent triangles have proportional lengths of corresponding sides:

$\dfrac{p}{a}= \dfrac{r}{c} =\dfrac{q}{b}.$

The second equality is the same as in option D.

Answer: correct choice is D.

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