Q. If triangle JKL is congruent to triangle MNO by the ASA criterion, what can be concluded about their sides?
A.
They are equal
B.
They are proportional
C.
They are similar
D.
Cannot be determined
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Solution
If two triangles are congruent by ASA (Angle-Side-Angle), then their corresponding sides are equal.
Correct Answer:
A
— They are equal
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Q. If triangle JKL is congruent to triangle MNO by the ASA criterion, which of the following is true?
A.
Angle J = Angle M
B.
Angle K = Angle N
C.
Side JL = Side MN
D.
All of the above
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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 congruent to triangle MNO by the SAS criterion, which of the following must be true?
A.
JK = MN
B.
KL = NO
C.
Angle J = Angle M
D.
All of the above
Show solution
Solution
By SAS, the two sides and the included angle are equal, so all corresponding parts are equal.
Correct Answer:
D
— All of the above
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Q. If triangle JKL is congruent to triangle MNO, which of the following is true?
A.
JK = MN
B.
KL = NO
C.
JL = MO
D.
All of the above
Show solution
Solution
Congruent triangles have all corresponding sides and angles equal, so all statements are true.
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?
A.
3:5
B.
9:25
C.
15:25
D.
6:10
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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 JKL is similar to triangle MNO, and the lengths of JK and MN are 5 cm and 10 cm respectively, what is the ratio of their areas?
A.
1:2
B.
1:4
C.
1:3
D.
2:1
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Solution
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (5/10)² = 1/4.
Correct Answer:
B
— 1:4
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Q. If triangle PQR is an isosceles triangle with PQ = PR, and the vertex angle Q is 40 degrees, what are the base angles?
A.
20 degrees
B.
40 degrees
C.
70 degrees
D.
80 degrees
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Solution
In an isosceles triangle, the base angles are equal. Therefore, the base angles are (180 - 40) / 2 = 70 degrees each.
Correct Answer:
D
— 80 degrees
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Q. If triangle PQR is an isosceles triangle with PQ = PR, which of the following is true?
A.
PQ = QR
B.
PR = QR
C.
Angle P = Angle Q
D.
Angle P = Angle R
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Solution
In an isosceles triangle, the angles opposite the equal sides are equal, so Angle P = Angle R.
Correct Answer:
D
— Angle P = Angle R
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Q. If triangle PQR is similar to triangle STU and the length of PQ is 12 cm while ST is 16 cm, what is the ratio of PQ to ST?
A.
3:4
B.
4:3
C.
12:16
D.
16:12
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Solution
The ratio of PQ to ST is 12:16, which simplifies to 3:4.
Correct Answer:
A
— 3:4
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Q. If triangle PQR is similar to triangle STU and the length of side PQ is 9 cm while side ST is 15 cm, what is the ratio of PQ to ST?
A.
3:5
B.
5:3
C.
9:15
D.
15:9
Show solution
Solution
The ratio of corresponding sides of similar triangles is PQ:ST = 9:15, which simplifies to 3:5.
Correct Answer:
A
— 3:5
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Q. If triangle PQR is similar to triangle STU, and the sides of triangle PQR are 3, 4, and 5, what are the lengths of the corresponding sides of triangle STU if the ratio is 2:1?
A.
6, 8, 10
B.
3, 4, 5
C.
1.5, 2, 2.5
D.
4, 5, 6
Show solution
Solution
If the ratio is 2:1, then the sides of triangle STU will be 3*2, 4*2, and 5*2, which are 6, 8, and 10.
Correct Answer:
A
— 6, 8, 10
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Q. If triangle STU is similar to triangle VWX, and ST = 5 cm, TU = 10 cm, and VW = 15 cm, what is the length of side WX?
A.
10 cm
B.
20 cm
C.
25 cm
D.
30 cm
Show solution
Solution
Since the triangles are similar, the ratio of corresponding sides is constant. Therefore, WX = (TU / ST) * VW = (10 / 5) * 15 = 2 * 15 = 30 cm.
Correct Answer:
B
— 20 cm
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Q. If triangle UVW is similar to triangle XYZ and UV = 3 cm, XY = 6 cm, what is the scale factor from triangle UVW to triangle XYZ?
A.
1:2
B.
2:1
C.
1:3
D.
3:1
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Solution
The scale factor is the ratio of corresponding sides: 3 cm to 6 cm is 1:2.
Correct Answer:
A
— 1:2
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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?
A.
70 degrees
B.
80 degrees
C.
60 degrees
D.
50 degrees
Show solution
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 triangle VWX is isosceles with VW = VX and angle W = 40 degrees, what is the measure of angle V?
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
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 triangle VWX is similar to triangle YZ, and the length of side VW is 10 cm while the corresponding side YZ is 15 cm, what is the ratio of the lengths of the sides?
A.
2:3
B.
3:2
C.
1:1.5
D.
1.5:1
Show solution
Solution
The ratio of the lengths of the sides is 10:15, which simplifies to 2:3.
Correct Answer:
A
— 2:3
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Q. If triangle VWX is similar to triangle YZ, and the length of side VW is 9 cm while side YZ is 3 cm, what is the scale factor from triangle YZ to triangle VWX?
A.
1:3
B.
3:1
C.
1:2
D.
2:1
Show solution
Solution
The scale factor from triangle YZ to triangle VWX is 9/3 = 3, so the scale factor is 3:1.
Correct Answer:
B
— 3:1
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Q. If triangle XYZ is congruent to triangle ABC, which of the following is true?
A.
XY = AB
B.
XZ = AC
C.
YZ = BC
D.
All of the above
Show solution
Solution
If two triangles are congruent, all corresponding sides and angles are equal, hence all statements are true.
Correct Answer:
D
— All of the above
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Q. If triangle XYZ is congruent to triangle PQR, which of the following is true?
A.
XY = PQ
B.
XZ = PR
C.
YZ = QR
D.
All of the above
Show solution
Solution
All corresponding sides and angles of congruent triangles are equal, so all statements are true.
Correct Answer:
D
— All of the above
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Q. If triangle XYZ is congruent to triangle PQR, which of the following statements is true?
A.
XY = PQ
B.
YZ = QR
C.
XZ = PR
D.
All of the above
Show solution
Solution
Congruent triangles have all corresponding sides and angles equal, so all statements are true.
Correct Answer:
D
— All of the above
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Q. If triangle XYZ is similar to triangle ABC and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?
A.
4:9
B.
2:3
C.
1:2
D.
3:2
Show solution
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:
A
— 4:9
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Q. If triangle XYZ is similar to triangle PQR and the length of XY is 5 cm and PQ is 10 cm, what is the ratio of their areas?
A.
1:2
B.
1:4
C.
1:5
D.
1:10
Show solution
Solution
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (5/10)² = 1/4.
Correct Answer:
B
— 1:4
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Q. If two angles are alternate exterior angles when two parallel lines are cut by a transversal, what can be concluded?
A.
They are equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are adjacent.
Show solution
Solution
Alternate exterior angles are equal when two parallel lines are cut by a transversal.
Correct Answer:
A
— They are equal.
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Q. If two angles are complementary, what is the sum of their measures?
A.
90 degrees
B.
180 degrees
C.
360 degrees
D.
270 degrees
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Solution
Complementary angles are two angles whose measures add up to 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. If two angles are corresponding angles formed by a transversal intersecting two parallel lines, what can be said about their measures?
A.
They are equal.
B.
They are complementary.
C.
They are supplementary.
D.
They are not related.
Show solution
Solution
Corresponding angles are equal when a transversal intersects two parallel lines.
Correct Answer:
A
— They are equal.
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Q. If two angles are corresponding angles formed by a transversal intersecting two parallel lines, what is their relationship?
A.
They are equal.
B.
They are complementary.
C.
They are supplementary.
D.
They are not related.
Show solution
Solution
Corresponding angles are equal when a transversal intersects two parallel lines.
Correct Answer:
A
— They are equal.
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Q. If two angles are corresponding angles when two parallel lines are cut by a transversal, what can be concluded?
A.
They are equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are adjacent.
Show solution
Solution
Corresponding angles are equal when two parallel lines are cut by a transversal.
Correct Answer:
A
— They are equal.
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Q. If two angles are supplementary and one angle measures 120°, what is the measure of the other angle?
A.
60°
B.
90°
C.
120°
D.
180°
Show solution
Solution
Supplementary angles sum to 180°. Therefore, the other angle = 180° - 120° = 60°.
Correct Answer:
A
— 60°
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Q. If two angles are supplementary and one angle measures 35 degrees, what is the measure of the other angle?
A.
145 degrees
B.
35 degrees
C.
90 degrees
D.
55 degrees
Show solution
Solution
Supplementary angles sum to 180 degrees, so the other angle is 180 - 35 = 145 degrees.
Correct Answer:
A
— 145 degrees
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Q. If two angles are supplementary and one angle measures 3x and the other measures 2x, what is the value of x?
Show solution
Solution
3x + 2x = 180°. Therefore, 5x = 180°; x = 36°. The question asks for x, which is 15.
Correct Answer:
B
— 15
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