Q1. Which of the following triangles is congruent to triangle ABC if angle A = angle D and side AB = side DE?
Solution:
By the Angle-Side-Angle (ASA) postulate, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
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Q2. What is the area of a triangle with a base of 6 units and a height of 4 units?
Solution:
The area A of a triangle is given by A = 1/2 * base * height = 1/2 * 6 * 4 = 12 square units.
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Q3. What is the area of a rectangle with a length of 5 units and a width of 3 units?
Solution:
The area of a rectangle is calculated using the formula A = length × width. Here, A = 5 × 3 = 15.
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Q4. What is the length of the hypotenuse of a right triangle with legs of lengths 6 and 8?
Solution:
Using the Pythagorean theorem, c = √(a² + b²) = √(6² + 8²) = √(36 + 64) = √100 = 10.
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Q5. What is the area of a triangle with a base of 8 units and a height of 5 units?
Solution:
The area of a triangle is calculated using the formula A = 1/2 * base * height. A = 1/2 * 8 * 5 = 20.
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Q6. Which of the following triangles is congruent to a triangle with sides 5, 12, and 13?
Solution:
A triangle with sides 5, 12, and 13 is congruent to itself.
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Q7. What is the volume of a cylinder with a radius of 2 units and a height of 5 units?
Solution:
The volume of a cylinder is calculated using the formula V = πr²h. Here, V = π(2)²(5) = π(4)(5) = 20π.
