Q. If the lengths of the sides of triangle ABC are in the ratio 3:4:5, what type of triangle is it?
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A.
Acute
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B.
Obtuse
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C.
Right
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D.
Equilateral
Solution
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
Correct Answer:
C
— Right
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Q. If triangle JKL is similar to triangle MNO, and the lengths of JK and MN are 5 cm and 10 cm respectively, what is the ratio of their areas?
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A.
1:2
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B.
1:4
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C.
1:3
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D.
2:1
Solution
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (5/10)² = 1/4.
Correct Answer:
B
— 1:4
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Q. If triangle VWX is isosceles with VW = VX and angle W = 40 degrees, what is the measure of angle V?
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A.
70 degrees
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B.
80 degrees
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C.
90 degrees
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D.
100 degrees
Solution
In an isosceles triangle, the base angles are equal. Therefore, angle V = (180 - 40) / 2 = 70 degrees.
Correct Answer:
B
— 80 degrees
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Q. If two triangles are congruent by the ASA criterion, what can be concluded about their sides?
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A.
They are all equal
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B.
They are all different
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C.
Some are equal
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D.
Cannot be determined
Solution
By the ASA (Angle-Side-Angle) criterion, if two triangles are congruent, then all their corresponding sides are equal.
Correct Answer:
A
— They are all equal
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Q. If two triangles are congruent by the ASA criterion, which of the following must be true?
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A.
Their corresponding sides are equal
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B.
Their corresponding angles are equal
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C.
Their areas are equal
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D.
All of the above
Solution
By the ASA criterion, if two triangles have two equal angles and the included side equal, then all corresponding sides and angles are equal.
Correct Answer:
A
— Their corresponding sides are equal
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Q. In triangle ABC, if AB = AC and angle A = 100 degrees, what is the measure of angles B and C?
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A.
40 degrees each
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B.
50 degrees each
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C.
60 degrees each
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D.
80 degrees each
Solution
In an isosceles triangle, angles B and C are equal. Therefore, angle B = angle C = (180 - 100) / 2 = 40 degrees.
Correct Answer:
A
— 40 degrees each
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Q. In triangle MNO, if MN = 12 cm, NO = 16 cm, and MO = 20 cm, what is the perimeter of triangle MNO?
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A.
40 cm
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B.
36 cm
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C.
32 cm
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D.
28 cm
Solution
The perimeter of a triangle is the sum of its sides. Therefore, perimeter = 12 + 16 + 20 = 48 cm.
Correct Answer:
A
— 40 cm
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Q. In triangle STU, if ST = 7 cm, TU = 24 cm, and SU = 25 cm, is triangle STU a right triangle?
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A.
Yes
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B.
No
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C.
Only if angle S is 90 degrees
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D.
Only if angle T is 90 degrees
Solution
Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625, which equals 25^2. Therefore, triangle STU is a right triangle.
Correct Answer:
A
— Yes
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