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Q1. In triangle XYZ, if XY = 8 cm, YZ = 6 cm, and XZ = 10 cm, what type of triangle is it?
Solution:
Triangle XYZ has all sides of different lengths (8 cm, 6 cm, 10 cm), so it is a scalene triangle.
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Q2. What is the perimeter of an equilateral triangle with a side length of 4 cm?
Solution:
Perimeter = 3 * side length = 3 * 4 = 12 cm.
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Q3. In triangle PQR, if angle P = 45 degrees and angle Q = 45 degrees, what is the type of triangle?
Solution:
Since two angles are equal, triangle PQR is an isosceles triangle.
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Q4. If triangle ABC is similar to triangle DEF with a scale factor of 2, and the area of triangle ABC is 50 cm², what is the area of triangle DEF?
Solution:
The area of similar triangles is proportional to the square of the scale factor. Area of DEF = 50 * (2^2) = 200 cm².
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Q5. In triangle GHI, if GH = 7 cm, HI = 24 cm, and GI = 25 cm, is triangle GHI a right triangle?
Solution:
Using the Pythagorean theorem, 7² + 24² = 49 + 576 = 625 = 25², so triangle GHI is a right triangle.
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Q6. If triangle ABC is congruent to triangle DEF, which of the following is true?
Solution:
If two triangles are congruent, all corresponding sides and angles are equal.
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