Q1. If two triangles are similar with a ratio of their sides as 2:3, what is the ratio of their areas?
Solution:
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2/3)^2 = 4/9.
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Q2. In triangle DEF, if DE = 5, EF = 12, and DF = 13, what type of triangle is it?
Solution:
Since 5^2 + 12^2 = 13^2 (25 + 144 = 169), triangle DEF is a right triangle.
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Q3. What is the cosine of a 60-degree angle?
Solution:
The cosine of 60 degrees is 0.5.
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Q4. If triangle GHI is similar to triangle JKL and the length of GH is 5 cm and JK is 10 cm, what is the ratio of their corresponding sides?
Solution:
The ratio of corresponding sides of similar triangles is equal to the ratio of any two corresponding sides. Therefore, the ratio is 5:10, which simplifies to 1:2.
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Q5. If triangle DEF is similar to triangle GHI, and the lengths of DE and GH are 4 cm and 8 cm respectively, what is the ratio of their areas?
Solution:
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (4/8)^2 = 1/4.
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Q6. In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, is triangle JKL a right triangle?
Solution:
By the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2, so triangle JKL is a right triangle.
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Q7. What is the sine of a 30-degree angle?
Solution:
The sine of 30 degrees is 0.5.
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Q8. If two triangles have sides in the ratio 3:4:5, what type of triangle are they?
Solution:
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
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Q9. If two angles of a triangle are 50 degrees and 70 degrees, what is the third angle?
Solution:
The third angle = 180 - (50 + 70) = 60 degrees.
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Q10. In a circle, if the radius is 5 cm, what is the circumference?
