Q1. If triangle GHI is similar to triangle JKL and the sides of triangle GHI are 3 cm, 4 cm, and 5 cm, what is the ratio of the sides of triangle JKL if the longest side is 10 cm?
Solution:
The ratio of the longest sides is 10 cm to 5 cm, which simplifies to 2:1. Therefore, the sides of triangle JKL are in the ratio 2:1.
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Q2. In triangle MNO, if MN = 12 cm, NO = 16 cm, and MO = 20 cm, is triangle MNO a right triangle?
Solution:
Using the Pythagorean theorem, 12² + 16² = 144 + 256 = 400 = 20², so triangle MNO is a right triangle.
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Q3. 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?
Solution:
The sides of triangle PQR are in the ratio 12:16:20 = 3:4:5, which matches triangle ABC, confirming similarity.
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Q4. In coordinate geometry, what is the distance between the points (1, 2) and (4, 6)?
