Q. In triangle DEF, if angle D = 30° and angle E = 45°, what is angle F?
-
A.
105°
-
B.
90°
-
C.
75°
-
D.
60°
Solution
Angle F = 180° - (30° + 45°) = 105°.
Correct Answer:
A
— 105°
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Q. In triangle DEF, if angle D = 30° and angle E = 45°, what is the measure of angle F?
-
A.
105°
-
B.
90°
-
C.
75°
-
D.
60°
Solution
Angle F = 180° - (30° + 45°) = 105°.
Correct Answer:
A
— 105°
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Q. In triangle DEF, if angle D = 30° and angle E = 70°, what is the measure of angle F?
-
A.
80°
-
B.
70°
-
C.
60°
-
D.
50°
Solution
Angle F = 180° - (30° + 70°) = 80°.
Correct Answer:
A
— 80°
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Q. In triangle DEF, if angle D = 40° and angle E = 70°, what is angle F?
-
A.
70°
-
B.
80°
-
C.
60°
-
D.
50°
Solution
Angle F = 180° - (40° + 70°) = 70°.
Correct Answer:
B
— 80°
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Q. In triangle DEF, if angle D = 40° and angle E = 70°, what is the measure of angle F?
-
A.
70°
-
B.
80°
-
C.
90°
-
D.
100°
Solution
Angle F = 180° - (40° + 70°) = 70°.
Correct Answer:
B
— 80°
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Q. In triangle DEF, if angle D = 45° and angle E = 45°, what is the type of triangle?
-
A.
Scalene
-
B.
Isosceles
-
C.
Equilateral
-
D.
Right
Solution
Since two angles are equal, triangle DEF is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if angle D = 45° and angle E = 45°, what type of triangle is DEF?
-
A.
Scalene
-
B.
Isosceles
-
C.
Equilateral
-
D.
Right
Solution
Since two angles are equal, triangle DEF is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if angle D = 45° and angle E = 45°, what type of triangle is it?
-
A.
Scalene
-
B.
Isosceles
-
C.
Equilateral
-
D.
Right
Solution
A triangle with two equal angles is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if DE = 10 cm, DF = 15 cm, and angle E = 45 degrees, what is the length of EF using the Law of Cosines?
-
A.
5√2 cm
-
B.
10√2 cm
-
C.
15√2 cm
-
D.
20 cm
Solution
Using the Law of Cosines: EF² = DE² + DF² - 2 * DE * DF * cos(E). EF² = 10² + 15² - 2 * 10 * 15 * cos(45°) = 100 + 225 - 150√2. Thus, EF = 5√2 cm.
Correct Answer:
A
— 5√2 cm
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Q. In triangle DEF, if DE = 10, DF = 6, and EF = 8, which side is the longest?
-
A.
DE
-
B.
DF
-
C.
EF
-
D.
All are equal
Solution
DE = 10 is the longest side since 10 > 8 and 10 > 6.
Correct Answer:
A
— DE
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Q. In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is the triangle a right triangle?
-
A.
Yes
-
B.
No
-
C.
Not enough information
-
D.
Only if angles are known
Solution
Using the Pythagorean theorem, 5² + 12² = 25 + 144 = 169 = 13², thus triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle DEF, if DE = 5, EF = 12, and DF = 13, what type of triangle is it?
-
A.
Equilateral
-
B.
Isosceles
-
C.
Right
-
D.
Scalene
Solution
Since 5^2 + 12^2 = 13^2 (25 + 144 = 169), triangle DEF is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle DEF, if DE = 6 cm, DF = 8 cm, and angle E = 90 degrees, what is the length of EF?
-
A.
10 cm
-
B.
12 cm
-
C.
14 cm
-
D.
16 cm
Solution
Using the Pythagorean theorem, EF = √(DE^2 + DF^2) = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, is triangle DEF a right triangle?
-
A.
Yes
-
B.
No
-
C.
Not enough information
-
D.
Only if DE is the longest side
Solution
By the Pythagorean theorem, if DE^2 + DF^2 = EF^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 DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, what is the area of the triangle?
-
A.
24 cm²
-
B.
30 cm²
-
C.
48 cm²
-
D.
60 cm²
Solution
Using Heron's formula, s = (6 + 8 + 10) / 2 = 12. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12*6*4*2] = √576 = 24 cm².
Correct Answer:
B
— 30 cm²
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Q. In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, what is the area of triangle DEF?
-
A.
24 cm²
-
B.
30 cm²
-
C.
48 cm²
-
D.
60 cm²
Solution
Using Heron's formula, the semi-perimeter s = (6 + 8 + 10) / 2 = 12 cm. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12*6*4*2] = √576 = 24 cm².
Correct Answer:
B
— 30 cm²
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Q. In triangle DEF, if DE = 6 cm, EF = 8 cm, and DF = 10 cm, is triangle DEF a right triangle?
-
A.
Yes
-
B.
No
-
C.
Cannot be determined
-
D.
Only if angle D is 90 degrees
Solution
Triangle DEF satisfies the Pythagorean theorem (6² + 8² = 10²), thus it is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle DEF, if DE = 6, DF = 8, and EF = 10, is triangle DEF a right triangle?
-
A.
Yes
-
B.
No
-
C.
Not enough information
-
D.
Only if DE is the hypotenuse
Solution
Using the Pythagorean theorem, 6² + 8² = 36 + 64 = 100 = 10², so triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle DEF, if DE = 6, DF = 8, and EF = 10, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 6² + 8² = 10², triangle DEF is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle DEF, if DE = 6, DF = 8, and EF = 10, what type of triangle is it?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Using the Pythagorean theorem, since 6² + 8² = 36 + 64 = 100 = 10², triangle DEF is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle DEF, if DE = 6, EF = 8, and DF = 10, is triangle DEF a right triangle?
-
A.
Yes
-
B.
No
-
C.
Not enough information
-
D.
Only if angle D is 90 degrees
Solution
Using the Pythagorean theorem, 6² + 8² = 36 + 64 = 100 = 10², thus triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, is triangle DEF a right triangle?
-
A.
Yes
-
B.
No
-
C.
Cannot be determined
-
D.
Only if angle D is 90 degrees
Solution
Using the Pythagorean theorem: 8² + 6² = 64 + 36 = 100 = 10², so triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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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?
-
A.
24 cm²
-
B.
30 cm²
-
C.
36 cm²
-
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?
-
A.
Equilateral
-
B.
Isosceles
-
C.
Scalene
-
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 angle G = 30 degrees and angle H = 60 degrees, what is the length of side GH if side GI = 10 cm?
-
A.
5 cm
-
B.
8.66 cm
-
C.
10 cm
-
D.
12 cm
Solution
Using the sine rule: GH/sin(30) = GI/sin(60). Therefore, GH = 10 * sin(30)/sin(60) = 10 * 0.5/(√3/2) = 10 * 1/√3 = 10/√3 ≈ 8.66 cm.
Correct Answer:
B
— 8.66 cm
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Q. In triangle GHI, if angle G = 30° and angle H = 45°, what is the measure of angle I?
-
A.
105°
-
B.
90°
-
C.
75°
-
D.
60°
Solution
The sum of angles in a triangle is 180°. Therefore, angle I = 180° - (30° + 45°) = 105°.
Correct Answer:
A
— 105°
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Q. In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side g opposite angle G if side h opposite angle H is 10 units?
Solution
Using the sine rule: g/h = sin(G)/sin(H) => g/10 = sin(30°)/sin(60°) => g = 10 * (1/2) / (√3/2) = 10/√3 = 8.66.
Correct Answer:
B
— 8.66
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Q. In triangle GHI, if angle G = 30° and angle H = 70°, what is the measure of angle I?
-
A.
80°
-
B.
60°
-
C.
50°
-
D.
40°
Solution
The sum of angles in a triangle is 180°. Therefore, angle I = 180° - (30° + 70°) = 80°.
Correct Answer:
B
— 60°
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Q. In triangle GHI, if angle G = 45 degrees and angle H = 45 degrees, what type of triangle is it?
-
A.
Scalene
-
B.
Isosceles
-
C.
Equilateral
-
D.
Right
Solution
A triangle with two equal angles is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle GHI, if angle G = 50 degrees and angle H = 70 degrees, what is the length of side GH if side GI = 10 cm?
-
A.
5 cm
-
B.
10 cm
-
C.
15 cm
-
D.
20 cm
Solution
Using the Law of Sines, GH / sin(I) = GI / sin(G). Since angles sum to 180, angle I = 60 degrees. Thus, GH = 10 * sin(60) / sin(50).
Correct Answer:
B
— 10 cm
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