Q. If triangle JKL is congruent to triangle MNO by the ASA criterion, which of the following is true?
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A.
Angle J = Angle M
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B.
Angle K = Angle N
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C.
Side JL = Side MN
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D.
All of the above
Solution
By the ASA criterion, if two triangles have two angles and the included side equal, then all corresponding angles and sides are equal.
Correct Answer:
D
— All of the above
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Q. If triangle JKL is similar to triangle MNO and the ratio of their corresponding sides is 3:5, what is the ratio of their areas?
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A.
3:5
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B.
9:25
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C.
15:25
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D.
6:10
Solution
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (3/5)² = 9/25.
Correct Answer:
B
— 9:25
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Q. If triangle VWX is an isosceles triangle 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.
60 degrees
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D.
50 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 SSS criterion, which of the following must be true?
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A.
Their angles are equal
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B.
Their sides are equal
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C.
Their areas are equal
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D.
All of the above
Solution
By the SSS criterion, if two triangles have all three sides equal, then their corresponding sides are equal.
Correct Answer:
B
— Their sides are equal
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Q. In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, what is the area of the triangle?
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A.
24 cm²
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B.
30 cm²
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C.
36 cm²
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D.
48 cm²
Solution
Using Heron's formula, s = (8 + 6 + 10) / 2 = 12 cm. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-8)(12-6)(12-10)] = √[12*4*6*2] = √144 = 12 cm².
Correct Answer:
B
— 30 cm²
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Q. In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, what type of triangle is DEF?
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A.
Equilateral
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B.
Isosceles
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C.
Scalene
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D.
Right
Solution
Since all sides are of different lengths, triangle DEF is a scalene triangle.
Correct Answer:
C
— Scalene
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Q. In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, what is the area of triangle GHI using Heron's formula?
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A.
96 cm²
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B.
96√3 cm²
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C.
48 cm²
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D.
64 cm²
Solution
First, calculate the semi-perimeter s = (12 + 16 + 20) / 2 = 24 cm. Then, area = √[s(s-a)(s-b)(s-c)] = √[24(24-12)(24-16)(24-20)] = √[24*12*8*4] = 96 cm².
Correct Answer:
A
— 96 cm²
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Q. In triangle GHI, if GH = 5 cm, HI = 12 cm, and GI = 13 cm, is triangle GHI a right triangle?
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A.
Yes
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B.
No
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C.
Not enough information
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D.
Only if angle G is 90 degrees
Solution
Using the Pythagorean theorem, 5² + 12² = 25 + 144 = 169 = 13², thus triangle GHI is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle PQR, if angle P = 30 degrees and angle Q = 45 degrees, what is the length of side QR if PQ = 10 cm?
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A.
5√2 cm
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B.
10 cm
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C.
10√2 cm
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D.
5 cm
Solution
Using the sine rule, QR = PQ * (sin Q / sin P) = 10 * (sin 45 / sin 30) = 10 * (√2/2 / 1/2) = 10√2 cm.
Correct Answer:
A
— 5√2 cm
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Q. In triangle PQR, if PQ = 7 cm, PR = 24 cm, and QR = 25 cm, 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
Using the Pythagorean theorem, 7² + 24² = 49 + 576 = 625 = 25², thus triangle PQR is a right triangle.
Correct Answer:
C
— Right
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Q. What is the length of the altitude from vertex A to side BC in triangle ABC if AB = 10 cm, AC = 6 cm, and angle A = 30 degrees?
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A.
3 cm
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B.
5 cm
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C.
6 cm
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D.
10 cm
Solution
The altitude h = AC * sin(A) = 6 * sin(30°) = 6 * 0.5 = 3 cm.
Correct Answer:
B
— 5 cm
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Q. Which of the following pairs of triangles are congruent by the ASA criterion?
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A.
Angle A = 30°, Angle B = 60°, Side AB = 5 cm
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B.
Angle A = 30°, Angle B = 60°, Side AC = 5 cm
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C.
Angle A = 60°, Angle B = 30°, Side AB = 5 cm
-
D.
Angle A = 60°, Angle B = 30°, Side AC = 5 cm
Solution
For ASA, two angles and the included side must be equal. The second option meets this criterion.
Correct Answer:
B
— Angle A = 30°, Angle B = 60°, Side AC = 5 cm
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Q. Which of the following statements is true for similar triangles?
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A.
Their corresponding angles are equal
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B.
Their corresponding sides are proportional
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C.
Both A and B
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D.
None of the above
Solution
Similar triangles have equal corresponding angles and proportional corresponding sides.
Correct Answer:
C
— Both A and B
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