Q. In triangle GHI, if angle G = 70° and angle H = 40°, what is the measure of angle I?
A.
70°
B.
60°
C.
50°
D.
30°
Show solution
Solution
Angle I = 180° - (70° + 40°) = 70°.
Correct Answer:
B
— 60°
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Q. In triangle GHI, if angle G is 45 degrees and angle H is 45 degrees, what type of triangle is it?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal, triangle GHI is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle GHI, if angle G is 45 degrees and side GH is 5 cm, what is the length of side HI if triangle GHI is a right triangle?
A.
5 cm
B.
5√2 cm
C.
10 cm
D.
2.5 cm
Show solution
Solution
In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, so HI = GH√2 = 5√2 cm.
Correct Answer:
B
— 5√2 cm
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Q. In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, is triangle GHI a right triangle?
A.
Yes
B.
No
C.
Only if angle G is 90 degrees
D.
Only if angle H is 90 degrees
Show solution
Solution
Using the Pythagorean theorem, 12² + 16² = 144 + 256 = 400 = 20², so triangle GHI is a right triangle.
Correct Answer:
A
— Yes
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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?
A.
96 cm²
B.
96√3 cm²
C.
48 cm²
D.
64 cm²
Show solution
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 = 12 cm, HI = 16 cm, and GI = 20 cm, what is the area of triangle GHI?
A.
48 cm²
B.
96 cm²
C.
60 cm²
D.
80 cm²
Show solution
Solution
Using Heron's formula, s = (12 + 16 + 20) / 2 = 24 cm. Area = √(s(s-a)(s-b)(s-c)) = √(24(24-12)(24-16)(24-20)) = √(24*12*8*4) = 96 cm².
Correct Answer:
B
— 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?
A.
Yes
B.
No
C.
Not enough information
D.
Only if angle G is 90 degrees
Show solution
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 GHI, if GH = 5 cm, HI = 12 cm, and GI = 13 cm, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169, which equals 13^2. Therefore, triangle GHI is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle GHI, if GH = 7 cm, HI = 10 cm, and GI = 5 cm, is triangle GHI a right triangle?
A.
Yes
B.
No
C.
Only if angle G is 90 degrees
D.
Only if angle H is 90 degrees
Show solution
Solution
Using the Pythagorean theorem, 7² + 5² = 49 + 25 = 74, and 10² = 100. Since 74 ≠ 100, triangle GHI is not a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle GHI, if GH = 7 cm, HI = 10 cm, and GI = 5 cm, which side is the longest?
A.
GH
B.
HI
C.
GI
D.
All sides are equal
Show solution
Solution
HI is the longest side as it measures 10 cm, which is greater than both GH and GI.
Correct Answer:
B
— HI
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Q. In triangle GHI, if GH = 7 cm, HI = 24 cm, and GI = 25 cm, is triangle GHI a right triangle?
A.
Yes
B.
No
C.
Not enough information
D.
Only if angle G is 90 degrees
Show solution
Solution
Using the Pythagorean theorem, 7² + 24² = 49 + 576 = 625 = 25², so triangle GHI is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle GHI, if GH = 8, HI = 6, and GI = 10, is triangle GHI a right triangle?
A.
Yes
B.
No
C.
Not enough information
D.
Only if angle G is 90 degrees
Show solution
Solution
Using the Pythagorean theorem: 8² + 6² = 64 + 36 = 100 = 10², so triangle GHI is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle GHI, if GH = 9 cm, HI = 12 cm, and GI = 15 cm, is triangle GHI a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle G is 90 degrees
Show solution
Solution
Yes, because 9² + 12² = 81 + 144 = 225 = 15², satisfying the Pythagorean theorem.
Correct Answer:
A
— Yes
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Q. In triangle JKL, if angle J = 80° and angle K = 50°, what is angle L?
A.
50°
B.
60°
C.
70°
D.
80°
Show solution
Solution
Angle L = 180° - (80° + 50°) = 50°.
Correct Answer:
C
— 70°
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Q. In triangle JKL, if angle J = 90° and angle K = 45°, what is the measure of angle L?
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
In a right triangle, the sum of the angles is 180°. Therefore, angle L = 180° - (90° + 45°) = 45°.
Correct Answer:
B
— 45°
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Q. In triangle JKL, if JK = 12 cm, KL = 16 cm, and JL = 20 cm, what is the perimeter of the triangle?
A.
28 cm
B.
36 cm
C.
40 cm
D.
48 cm
Show solution
Solution
Perimeter = JK + KL + JL = 12 + 16 + 20 = 48 cm.
Correct Answer:
B
— 36 cm
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Q. In triangle JKL, if JK = 12 cm, KL = 16 cm, and JL = 20 cm, what is the semi-perimeter of the triangle?
A.
24 cm
B.
28 cm
C.
30 cm
D.
32 cm
Show solution
Solution
Semi-perimeter = (JK + KL + JL) / 2 = (12 + 16 + 20) / 2 = 28 cm.
Correct Answer:
B
— 28 cm
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Q. In triangle JKL, if JK = 12 cm, KL = 16 cm, and JL = 20 cm, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
It is a right triangle because 12² + 16² = 144 + 256 = 400 = 20².
Correct Answer:
C
— Right
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Q. In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, is triangle JKL a right triangle?
A.
Yes
B.
No
C.
Not enough information
D.
Only if angle J is 90 degrees
Show solution
Solution
By the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2, so triangle JKL is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle JKL, if JK = 6 cm, KL = 8 cm, and JL = 10 cm, is triangle JKL a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle K is 90 degrees
Show solution
Solution
By the Pythagorean theorem, if JK^2 + KL^2 = JL^2, then it is a right triangle. 6^2 + 8^2 = 36 + 64 = 100 = 10^2.
Correct Answer:
A
— Yes
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Q. In triangle JKL, if JK = 8 cm, KL = 6 cm, and JL = 10 cm, is triangle JKL a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angles are known
Show solution
Solution
Using the Pythagorean theorem, 8² + 6² = 64 + 36 = 100 = 10², so triangle JKL is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle JKL, if JK = 8, KL = 6, and JL = 10, is triangle JKL a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angles are known
Show solution
Solution
Using the Pythagorean theorem: 8² + 6² = 64 + 36 = 100 = 10², so triangle JKL is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle MNO, if angle M = 45 degrees and angle N = 45 degrees, what type of triangle is MNO?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal, triangle MNO is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle MNO, if MN = 12 cm, NO = 16 cm, and angle M = 60 degrees, what is the length of MO using the Law of Cosines?
A.
8 cm
B.
10 cm
C.
12 cm
D.
14 cm
Show solution
Solution
Using the Law of Cosines: MO² = MN² + NO² - 2 * MN * NO * cos(M). MO² = 12² + 16² - 2 * 12 * 16 * cos(60°) = 144 + 256 - 192 = 208. Thus, MO = √208 = 10 cm.
Correct Answer:
B
— 10 cm
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Q. In triangle MNO, if MN = 12 cm, NO = 16 cm, and MO = 20 cm, is triangle MNO a right triangle?
A.
Yes
B.
No
C.
Only if angle M is 90 degrees
D.
Only if angle N is 90 degrees
Show solution
Solution
Using the Pythagorean theorem, 12² + 16² = 144 + 256 = 400 = 20², so triangle MNO is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle MNO, if MN = 12 cm, NO = 16 cm, and MO = 20 cm, prove that triangle MNO is congruent to triangle PQR with sides PQ = 12 cm, QR = 16 cm, and PR = 20 cm.
A.
By SSS
B.
By SAS
C.
By ASA
D.
Not congruent
Show solution
Solution
Both triangles have sides of equal lengths (12 cm, 16 cm, 20 cm), thus they are congruent by the SSS criterion.
Correct Answer:
A
— By SSS
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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?
A.
40 cm
B.
36 cm
C.
32 cm
D.
28 cm
Show solution
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 MNO, if MN = 5 cm, NO = 12 cm, and MO = 13 cm, is triangle MNO a right triangle?
A.
Yes
B.
No
C.
Not enough information
D.
Only if angle M is 90 degrees
Show solution
Solution
Using the Pythagorean theorem, 5² + 12² = 25 + 144 = 169 = 13², so triangle MNO 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 PR if PQ = 10 cm?
A.
5 cm
B.
7.5 cm
C.
8.66 cm
D.
10 cm
Show solution
Solution
Using the sine rule, PR = PQ * (sin(Q) / sin(P)) = 10 * (sin(45) / sin(30)) = 10 * (√2/2 / 1/2) = 10 * √2 = 8.66 cm.
Correct Answer:
C
— 8.66 cm
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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?
A.
5√2 cm
B.
10 cm
C.
10√2 cm
D.
5 cm
Show solution
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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