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 of the following triangles is similar to a triangle with angles 30°, 60°, and 90°?
A.
30°, 60°, 90°
B.
45°, 45°, 90°
C.
60°, 30°, 90°
D.
90°, 30°, 60°
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Solution
Triangles are similar if they have the same angles. The triangle with angles 30°, 60°, and 90° is similar to itself.
Correct Answer:
A
— 30°, 60°, 90°
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Q. Which of the following triangles is similar to triangle ABC if angle A = angle D and angle B = angle E?
A.
Triangle DEF
B.
Triangle GHI
C.
Triangle JKL
D.
Triangle MNO
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Solution
By the Angle-Angle (AA) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
Correct Answer:
A
— Triangle DEF
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Q. Which of the following triangles is similar to triangle ABC with angles 30°, 60°, and 90°?
A.
30°, 60°, 90°
B.
45°, 45°, 90°
C.
60°, 60°, 60°
D.
30°, 30°, 120°
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Solution
Triangles are similar if they have the same angles. Triangle ABC has angles 30°, 60°, and 90°, so it is similar to any triangle with the same angles.
Correct Answer:
A
— 30°, 60°, 90°
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Q. Which of the following values satisfies the inequality: -3x + 6 < 0?
A.
x = 1
B.
x = 2
C.
x = -1
D.
x = -2
Show solution
Solution
Step 1: Subtract 6 from both sides: -3x < -6. Step 2: Divide by -3 (reverse the inequality): x > 2. Thus, x = 2 satisfies the inequality.
Correct Answer:
B
— x = 2
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Q. Which of the following values satisfies the inequality: 3x + 4 < 10?
A.
x = 1
B.
x = 2
C.
x = 3
D.
x = 4
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Solution
Step 1: Subtract 4 from both sides: 3x < 6. Step 2: Divide by 3: x < 2.
Correct Answer:
A
— x = 1
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Q. Which of the following values satisfies the inequality: 4 - x > 1?
A.
x < 3
B.
x > 3
C.
x = 3
D.
x ≤ 3
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Solution
Step 1: Subtract 4 from both sides: -x > -3. Step 2: Multiply by -1 (reverse inequality): x < 3.
Correct Answer:
A
— x < 3
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Q. Which of the following values satisfies the inequality: 4x - 1 < 3?
A.
x = 1
B.
x = 0
C.
x = 2
D.
x = -1
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Solution
Step 1: Add 1 to both sides: 4x < 4. Step 2: Divide by 4: x < 1. Therefore, x = 0 satisfies the inequality.
Correct Answer:
B
— x = 0
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Q. Which of the following values satisfies the inequality: 4x - 1 < 3x + 2?
A.
x < 3
B.
x > 3
C.
x < 1
D.
x > 1
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Solution
Step 1: Subtract 3x from both sides: x - 1 < 2. Step 2: Add 1: x < 3.
Correct Answer:
D
— x > 1
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Q. Which of the following values satisfies the inequality: 5 - 2x > 1?
A.
x < 2
B.
x > 2
C.
x < 1
D.
x > 1
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Solution
Step 1: Subtract 5 from both sides: -2x > -4. Step 2: Divide by -2 (reverse inequality): x < 2.
Correct Answer:
A
— x < 2
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Q. Which of the following values satisfies the inequality: 5 - x > 2?
A.
x < 3
B.
x > 3
C.
x < 5
D.
x > 5
Show solution
Solution
Step 1: Subtract 5 from both sides: -x > -3. Step 2: Multiply by -1 (reverse the inequality): x < 3.
Correct Answer:
A
— x < 3
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Q. Which of the following values satisfies the inequality: x/3 + 2 < 5?
A.
x < 9
B.
x > 9
C.
x = 9
D.
x = 6
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Solution
Step 1: Subtract 2 from both sides: x/3 < 3. Step 2: Multiply by 3: x < 9.
Correct Answer:
A
— x < 9
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Q. Which polynomial has a root at x = -1?
A.
x^2 + 2x + 1
B.
x^2 - 2x + 1
C.
x^2 + x - 2
D.
x^2 - x - 2
Show solution
Solution
The polynomial x^2 + 2x + 1 can be factored as (x + 1)(x + 1), indicating that -1 is a root.
Correct Answer:
A
— x^2 + 2x + 1
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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)
Show solution
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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