Q. If the lengths of the sides of triangle ABC are 3 cm, 4 cm, and 5 cm, what type of triangle is it?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right
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Solution
Triangle ABC is a right triangle because it satisfies the Pythagorean theorem: 3² + 4² = 5².
Correct Answer:
D
— Right
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Q. If triangle ABC is isosceles with AB = AC, which of the following is true?
A.
Angle B = Angle C
B.
Angle A = Angle B
C.
Angle A = Angle C
D.
All angles are equal
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Solution
In an isosceles triangle, the angles opposite the equal sides are also equal.
Correct Answer:
A
— Angle B = Angle C
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Q. If triangle ABC is similar to triangle DEF, and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?
A.
2:3
B.
4:9
C.
3:2
D.
9:4
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Solution
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2/3)² = 4/9.
Correct Answer:
B
— 4:9
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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
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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 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
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Solution
Perimeter = JK + KL + JL = 12 + 16 + 20 = 48 cm.
Correct Answer:
B
— 36 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 PR if PQ = 10 cm?
A.
5 cm
B.
7.5 cm
C.
8.66 cm
D.
10 cm
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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 = 90 degrees, what is angle R?
A.
60 degrees
B.
30 degrees
C.
90 degrees
D.
120 degrees
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Solution
Angle R = 180 - (30 + 90) = 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. In triangle XYZ, if XY = 8 cm, XZ = 6 cm, and YZ = 10 cm, which side is the longest?
A.
XY
B.
XZ
C.
YZ
D.
All sides are equal
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Solution
YZ is the longest side since 10 cm is greater than both 8 cm and 6 cm.
Correct Answer:
C
— YZ
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Q. What is the relationship between the sides of a right triangle?
A.
The sum of the two shorter sides equals the longest side
B.
The longest side is equal to the sum of the other two sides
C.
The square of the longest side equals the sum of the squares of the other two sides
D.
All sides are equal
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Solution
In a right triangle, the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides (Pythagorean theorem).
Correct Answer:
C
— The square of the longest side equals the sum of the squares of the other two sides
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Q. Which of the following statements is true for congruent triangles?
A.
They have the same area
B.
They have the same perimeter
C.
They have the same shape and size
D.
All of the above
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Solution
Congruent triangles have the same shape and size, which implies they also have the same area and perimeter.
Correct Answer:
D
— All of the above
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Q. Which of the following triangles is congruent to triangle DEF if DE = 5 cm, EF = 7 cm, and DF = 5 cm?
A.
Triangle GHI with GH = 5 cm, HI = 7 cm, GI = 5 cm
B.
Triangle JKL with JK = 6 cm, KL = 7 cm, JL = 5 cm
C.
Triangle MNO with MN = 5 cm, NO = 7 cm, MO = 6 cm
D.
Triangle PQR with PQ = 5 cm, QR = 5 cm, PR = 7 cm
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Solution
Triangles DEF and GHI are congruent by the Side-Side-Side (SSS) congruence criterion since they have the same side lengths.
Correct Answer:
A
— Triangle GHI with GH = 5 cm, HI = 7 cm, GI = 5 cm
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Q. Which theorem can be used to prove that two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle?
A.
Angle-Angle-Angle (AAA)
B.
Side-Angle-Side (SAS)
C.
Side-Side-Side (SSS)
D.
Angle-Side-Angle (ASA)
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Solution
The Side-Angle-Side (SAS) theorem can be used to prove the congruence of the triangles.
Correct Answer:
B
— Side-Angle-Side (SAS)
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