Q. If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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Solution
A triangle with sides a, b, and c (where c is the longest side) is a right triangle if a² + b² = c². Here, 5² + 12² = 25 + 144 = 169 = 13², so it is a right triangle.
Correct Answer:
C
— Right
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Q. If two triangles are similar, what is true about their corresponding angles?
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are different
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Solution
In similar triangles, corresponding angles are equal.
Correct Answer:
A
— They are equal
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Q. What is the area of a trapezoid with bases of lengths 5 and 7 units and a height of 4 units?
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Solution
The area A of a trapezoid is given by the formula: A = 0.5 * (base1 + base2) * height. Here, A = 0.5 * (5 + 7) * 4 = 0.5 * 12 * 4 = 24.
Correct Answer:
A
— 24
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Q. What is the area of a trapezoid with bases of lengths 6 and 10 units and a height of 4 units?
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Solution
The area of a trapezoid is given by the formula: Area = 0.5 * (base1 + base2) * height. Here, Area = 0.5 * (6 + 10) * 4 = 0.5 * 16 * 4 = 32.
Correct Answer:
A
— 32
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Q. What is the equation of a line with a slope of 2 that passes through the point (1, 1)?
A.
y = 2x + 1
B.
y = 2x - 1
C.
y = 2x + 2
D.
y = 2x - 2
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Solution
Using the point-slope form of the equation of a line: y - y1 = m(x - x1), we have y - 1 = 2(x - 1). Simplifying gives y = 2x - 2 + 1, or y = 2x - 1.
Correct Answer:
A
— y = 2x + 1
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Q. What is the perimeter of a square with a side length of 4 units?
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Solution
The perimeter P of a square is given by the formula: P = 4 * side length. Here, P = 4 * 4 = 16.
Correct Answer:
C
— 16
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