Question

Are any two of the three triangles similar? if so write the appropriate similarity statement.​

Answer 1

Yes, triangle ABC is similar to triangle PQR

Yes, two of the three triangles are similar.

In triangle ABC, AB=5, AC=4, and BC=4.

In triangle PQR, PR=8, PQ=10, and angle RPQ=
`\(\theta\).`

To determine if two triangles are similar, we compare the ratios of their corresponding side lengths.

Here, the ratio of AB to PQ is
`\((5)/(10)\), which simplifies to \((1)/(2)\)`, and the ratio of AC to QR is
`\((4)/(8)\),`which also simplifies to
`\((1)/(2)\).`

Since both ratios are equal, triangle ABC is similar to triangle PQR.

The appropriate similarity statement is:
`\(\triangle ABC \sim \triangle PQR\).`

Answer 2

Angle ABC is similar to PQR.

Postulate is Side side, side similarity

Explanation:

In triangle ABC, AC:AB = 4/5 = 0.8

In triangle PQR, PR:PQ = 8/10 = 0.8

Looking at the triangle PQR carefully, we can deduce that QR = PR.

Thus; QR:PQ = 8/10 = 0.8.

Also,BC/AB = 4/5 = 0.8

Also, PR/RQ = 8/8 = 1 and AC/CB = 4/4 = 1

Both triangles have the same proportion of their sides and thus we can say they are similar.

Postulate used is Side, Side, Side similarity.