In triangle PQR, if PQ = 12 cm, PR = 16 cm, and QR = 20 cm, is triangle PQR simi

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Question: In triangle PQR, if PQ = 12 cm, PR = 16 cm, and QR = 20 cm, is triangle PQR similar to triangle ABC with sides 3 cm, 4 cm, and 5 cm?

Options:

Correct Answer: Yes

Solution:

The sides of triangle PQR are in the ratio 12:16:20 = 3:4:5, which matches triangle ABC, confirming similarity.

In triangle PQR, if PQ = 12 cm, PR = 16 cm, and QR = 20 cm, is triangle PQR similar to triangle ABC with sides 3 cm, 4 cm, and 5 cm?

In triangle PQR, if PQ = 12 cm, PR = 16 cm, and QR = 20 cm, is triangle PQR similar to triangle ABC with sides 3 cm, 4 cm, and 5 cm?

Step 1: Identify the sides of triangle PQR. They are PQ = 12 cm, PR = 16 cm, and QR = 20 cm.
Step 2: Identify the sides of triangle ABC. They are 3 cm, 4 cm, and 5 cm.
Step 3: Write down the ratios of the sides of triangle PQR. The ratios are PQ:PR:QR = 12:16:20.
Step 4: Simplify the ratios of triangle PQR. Divide each side by 4: 12/4 = 3, 16/4 = 4, 20/4 = 5. So, the simplified ratio is 3:4:5.
Step 5: Compare the simplified ratio of triangle PQR (3:4:5) with the sides of triangle ABC (3:4:5).
Step 6: Since the ratios are the same, conclude that triangle PQR is similar to triangle ABC.

Triangle Similarity – Triangles are similar if their corresponding sides are in proportion.
Ratio Comparison – Understanding how to simplify ratios to determine similarity.