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WorksheetsPRACTICE BENCHMARK
Total questions: 75
Worksheet time: 56mins
Name
Class
Date
1.
Which of the following statements is true regarding congruent triangles?
a)
A) Congruent triangles must have the same size but do not need to have the same shape.
b)
B) Congruent triangles must have corresponding sides and angles that are equal.
c)
C) Congruent triangles can only be proven congruent using angle-side-angle (ASA).
d)
D) Congruent triangles can only be proved using side-side-side (SSS).
2.
What is the definition of congruence in terms of rigid motions
a)
A) Two figures are congruent if they have the same area.
b)
B) Two figures are congruent if one can be transformed into the other through a series of rigid motions (translations, rotations, reflections).
c)
C) Two figures are congruent if their corresponding angles are equal.
d)
D) Two figures are congruent if they are similar in shape.
3.
If t △ABC is congruent to △DEF, which of the following pairs are necessarily congruent?
a)
A)∠A and ∠D
b)
B) AB and DE
c)
C) ∠C and ∠ F
d)
D) All of the above
4.
What is a rigid motion?
a)
A) A transformation that changes the size of a figure.
b)
B) A transformation that preserves distances and angles.
c)
C) A transformation that distorts a figure.
d)
D) A transformation that reflects a figure.
5.
What can you conclude if two triangles are proven to be congruent?
a)
A) Their angles must be equal.
b)
B) Their corresponding sides must be equal.
c)
C) Both A and B
d)
D) None of the above.
6.
What does CPCTC stand for?
a)
A) Corresponding Parts of Congruent Triangles are Congruent
b)
B) Corresponding Parts of Congruent Triangles are Similar
c)
C) Congruent Parts of Corresponding Triangles are Congruent
d)
D) None of the above
7.
Which rigid motion can be used to demonstrate that △XYZ is congruent to △PQR?
a)
A) A reflection across a line
b)
B) A translation of the entire triangle
c)
C) A rotation around a point
d)
D) All of the above
8.
If △JKL is congruent to △MNO, which of the following is true?
a)
A) JL = MN
b)
B)∠K = ∠O
c)
C) All corresponding sides and angles are congruent.
d)
D) All of the above.
9.
If △DEF is congruent to △GHI, what can be concluded about segment DE?
a)
A) DE = GH
b)
B) DE = HI
c)
C) DE ≠ GH
d)
D) DE and GH are not related.
10.
If two triangles have two pairs of corresponding angles equal, what can you conclude about the third pair of angles?
a)
A) They are equal.
b)
B) They are not necessarily equal.
c)
C) They are supplementary.
d)
D) There is not enough information.
11.
If △PQR is congruent to △STU, which of the following statements is false?
a)
A) ∠P = ∠ S
b)
B) Side QR = Side TU
c)
C) Side PQ = Side ST
d)
D) ∠R = ∠T
12.
How many pairs of corresponding angles are congruent if two triangles are congruent?
a)
A) One
b)
B) Two
c)
C) Three
d)
D) None
13.
Which of the following transformations is NOT a rigid motion?
a)
A) Reflection
b)
B) Rotation
c)
C) Dilation
d)
D) Translation
14.
If two triangles are congruent, how many pairs of corresponding sides are congruent?
a)
A) One
b)
B) Two
c)
C) Three
d)
D) None
15.
Which of the following is a necessary condition for using CPCTC?
a)
A) The triangles must be similar.
b)
B) The triangles must be congruent first.
c)
C) All angles must be equal.
d)
D) At least one side must be equal.
16.
If ΔABC ≅ ΔDEF and you know AB ≅ DE and BC ≅ EF, what can you conclude about ∠B?
a)
A) ∠B ≅ ∠D
b)
B) ∠B ≅ ∠E
c)
C) ∠B ≅ ∠F
d)
D) ∠B ≅ ∠A
17.
If two triangles are congruent, what can be said about their corresponding sides?
a)
A) They are equal in length
b)
B) They are perpendicular
c)
C) They are proportional
d)
D) They are parallel
18.
If ∆ABC ≅ ∆DEF, which of the following statements is true?
a)
A) ∠A = ∠E
b)
B) ∠B = ∠F
c)
C) ∠C = ∠D
d)
D) ∠A = ∠D
19.
Two triangles are congruent by the SAS theorem. Which statement follows by CPCTC?
a)
A) The triangles have equal perimeters
b)
B) Their corresponding angles are equal
c)
C) Their areas are equal
d)
D) Their diagonals are equal
20.
Given ∆PQR ≅ ∆XYZ, which of the following is true?
a)
A) PQ = XZ
b)
B) QR = XY
c)
C) PR = XZ
d)
D) ∠P = ∠X
21.
Which congruence condition can be used to prove ∆ABC ≅ ∆XYZ?
a)
A) AA
b)
B) SSS
c)
C) SSA
d)
D) AAA
22.
CPCTC is used after proving which of the following?
a)
A) Triangles are similar
b)
B) Triangles are congruent
c)
C) Triangles are proportional
d)
D) Triangles have equal areas
23.
After proving two triangles congruent using SSS, what can you conclude using CPCTC?
a)
A) Corresponding sides are congruent
b)
B) Corresponding angles are congruent
c)
C) Both A and B
d)
D) Neither A nor B
24.
CPCTC is most often used in which step of a geometric proof?
a)
A) The first step
b)
B) The last step
c)
C) The middle step
d)
D) It is not used in geometric proofs
25.
If ∆SIR ≅ ∆MAN, which of the following is true by CPCTC?
a)
A) ∠S = ∠M
b)
B) ∠I = ∠A
c)
C) ∠R = ∠N
d)
D) All of the above
26.
Which postulate 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)
A) SSS (Side-Side-Side)
b)
B) SAS (Side-Angle-Side)
c)
C) ASA (Angle-Side-Angle)
d)
D) AAS (Angle-Angle-Side)
27.
If two inscribed angles intercept the same arc, what can be said about the two angles?
a)
A) They are equal
b)
B) One is double the other
c)
C) They are complementary
d)
D) They are supplementary
28.
What is an inscribed angle?
a)
A) An angle whose vertex is at the center of the circle
b)
B) An angle whose vertex is on the circle and whose sides contain chords of the circle
c)
C) An angle whose vertex is outside the circle
d)
D) An angle whose vertex is on the radius of the circle
29.
The measure of an inscribed angle is always __________ the measure of the central angle that intercepts the same arc.
a)
A) Half
b)
B) Double
c)
C) Equal to
d)
D) One-third
30.
What does the SSS Postulate state?
a)
A) If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
b)
B) If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
c)
C) If two sides and an angle not included between them of one triangle are equal to two sides and an angle not included between them of another triangle, then the triangles are congruent.
d)
D) None of the above.
31.
A circumscribed angle is an angle formed by two lines that are __________ to a circle.
a)
A) Chords
b)
B) Secants
c)
C) Tangents
d)
D) Radii
32.
An inscribed angle subtends an arc of 80°. What is the measure of the inscribed angle?
a)
A) 80°
b)
B) 40°
c)
C) 160°
d)
D) 60°
33.
If a central angle measures 120°, what is the measure of the intercepted arc?
a)
A) 120°
b)
B) 240°
c)
C) 60°
d)
D) 90°
34.
If two secants intersect outside a circle, what is the relationship between the angle formed and the intercepted arcs?
a)
A) The angle is equal to the larger arc
b)
B) The angle is equal to half the difference of the intercepted arcs
c)
C) The angle is equal to the sum of the arcs
d)
D) The angle is equal to half the sum of the intercepted arcs
35.
If an angle is inscribed in a circle and its sides pass through the endpoints of a diameter, what is the measure of the angle?
a)
A) 45°
b)
B) 90°
c)
C) 180°
d)
D) 60°
36.
In a circle, if a right angle is inscribed, what can be inferred about the arc it intercepts?
a)
A) The arc is a semicircle
b)
B) The arc measures 90°
c)
C) The arc is less than a semicircle
d)
D) The arc is greater than 180°
37.
If △XYZ is congruent to △ABC by the SSS Postulate, which of the following is true?
a)
A) XY=AB, XZ=AC, YZ=BC
b)
B) XY=AC, XZ=AB, YZ=BC
c)
C) XY= BC, XZ= AB, YZ= AC
d)
D) None of the above
38.
An inscribed angle that intercepts a semicircle must be what type of angle?
a)
A) An acute angle
b)
B) A right angle
c)
C) An obtuse angle
d)
D) A reflex angle
39.
If two triangles have two sides equal and the angle between those sides is equal, what can be concluded?
a)
A) The triangles are similar.
b)
B) The triangles are congruent by SAS.
c)
C) The triangles are not related.
d)
D) The triangles are right triangles.
40.
If △ABC is congruent to △DEF by SSS, which of the following must be true?
a)
A) AB= DE
b)
B) AC=DF
c)
C) BC= EF
d)
D) All of the above
41.
If △XYZ is congruent to △ABC by ASA, which of the following must be true?
a)
A) ∠X = ∠A
b)
B) ∠Y = ∠C
c)
C) XY= AC
d)
D) None of the above
42.
AAS Postulate requires:
a)
A) Two angles and a side not between them.
b)
B) Two sides and the included angle.
c)
C) Three sides.
d)
D) None of the above.
43.
Which postulate is sufficient to prove triangle congruence with the following information: AB=DE, AC=DF, and with one included ∠A=∠D?
a)
A) SSS
b)
B) SAS
c)
C) ASA
d)
D) AAS
44.
If △PQR is congruent to △STU by SAS, which of the following must be true?
a)
A) QP= ST
b)
B) QR=UT
c)
C) PR=SU
d)
D) None of the above
45.
Which of the following is NOT a valid triangle congruence postulate?
a)
A) SSS
b)
B) SAS
c)
C) AAA
d)
D) ASA
46.
If triangle JKL is congruent to triangle MNO by AAS, what can you say about their sides?
a)
A) They are equal.
b)
B) They are similar.
c)
C) They have the same perimeter.
d)
D) None of the above.
47.
Two triangles are congruent if they have:
a)
A) Three equal angles.
b)
B) Two equal sides and the included angle.
c)
C) Two equal angles and a non-included side.
d)
D) All of the above.
48.
If △ABC≅△DEF by ASA, which pair of angles is equal?
a)
A) ∠A and ∠𝐷
b)
B) ∠B and∠𝐸
c)
C) Both A and B
d)
D) None of the above
49.
If ∠A=∠D, AB=DE, and ∠B=∠E what postulate can be applied?
a)
A) SSS
b)
B) SAS
c)
C) ASA
d)
D) AAS
50.
In right triangles, the HL theorem states that:
a)
A) If the hypotenuse and one angle are equal, then the triangles are congruent.
b)
B) If the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
c)
C) If two angles and a leg are equal, then the triangles are congruent.
d)
D) None of the above.
51.
Given two congruent triangles, ΔABC ≅ ΔDEF, which statement is false?
a)
A) ∠A ≅ ∠D
b)
B) ∠B ≅ ∠E
c)
C) AB ≅ DF
d)
D) AC ≅ DF
52.
If a radius is perpendicular to a tangent at the point of tangency, what type of angle is formed?
a)
A) Right angle
b)
B) Acute angle
c)
C) Obtuse angle
d)
D) Straight angle
53.
Which of the following is not a method for proving triangles congruent?
a)
A) SSS (Side-Side-Side)
b)
B) ASA (Angle-Side-Angle)
c)
C) SSA (Side-Side-Angle)
d)
D) AAS (Angle-Angle-Side)
54.
If ΔABC ≅ ΔDEF, which of the following must be true?
a)
A) AB ≅ DF
b)
B) ∠A ≅ ∠E
c)
C) BC ≅ EF
d)
D) ∠B ≅ ∠D
55.
If ΔMAN ≅ ΔHOP, which of the following must be true?
a)
A) AN ≅ PO
b)
B) ∠A ≅ ∠O
c)
C) MN ≅ OP
d)
D) ∠M ≅ ∠P
56.
Two triangles are congruent by the SSS Postulate. Which of the following statements is true?
a)
A) All pairs of angles are congruent
b)
B) Two pairs of sides are congruent
c)
C) One pair of angles is congruent
d)
D) None of the above
57.
Which of the following is a necessary condition for using the ASA Postulate?
a)
A)Two angles and a side not included between them
b)
B) Two sides and an included angle
c)
C) Two angles and the included side
d)
D) Three sides
58.
In which type of triangle can the HL theorem be applied?
a)
A) Isosceles triangle
b)
B) Scalene triangle
c)
C) Right triangle
d)
D) Equilateral triangle
59.
Which of the following is a requirement to use the HL theorem?
a)
A) Both triangles must have two sides equal.
b)
B) Both triangles must be right triangles.
c)
C) Both triangles must have three angles equal.
d)
D) Both triangles must have the same perimeter.
60.
When a radius intersects a tangent line at the point of tangency, what is the angle between them?
a)
A) 45°
b)
B) 60°
c)
C) 90°
d)
D) 180°
61.
Which of the following is true about triangles that are congruent by SSS?
a)
A) Their corresponding angles are equal.
b)
B) Their corresponding sides are equal.
c)
C) They must have the same area.
d)
D) Both A and B.
62.
What is a central angle?
a)
A) An angle whose vertex is on the circle
b)
B) An angle whose vertex is at the center of the circle
c)
C) An angle formed by two chords
d)
D) An angle outside the circle
63.
How is an inscribed angle defined?
a)
A) An angle formed by two radii
b)
B) An angle whose vertex is inside the circle
c)
C) An angle whose vertex is on the circle
d)
D) An angle whose vertex is outside the circle
64.
What is the relationship between a central angle and an inscribed angle that subtend the same arc?
a)
A) The central angle is half the inscribed angle.
b)
B) The inscribed angle is half the central angle.
c)
C) They are equal.
d)
D) There is no relationship.
65.
If the measure of a central angle is 120°, what is the measure of the inscribed angle that subtends the same arc?
a)
A) 60°
b)
B) 80°
c)
C) 160°
d)
C) 240°
66.
What is a circumscribed angle?
a)
A) An angle formed by two tangents to a circle
b)
B) An angle formed by two chords in a circle
c)
C) An angle with its vertex at the center of the circle
d)
D) An angle with its vertex inside the circle
67.
What can be said about the angle formed when a radius intersects a tangent at the point of tangency?
a)
A) The angle is 0°.
b)
B) The angle is 45°.
c)
C) The angle is 90°.
d)
D) The angle is 180°.
68.
How does the measure of a circumscribed angle relate to the inscribed angle subtending the same arc?
a)
A) They are equal.
b)
B) The circumscribed angle is twice the inscribed angle.
c)
C) The inscribed angle is twice the circumscribed angle.
d)
D) There is no relationship.
69.
If a line is tangent to a circle, how many points on the circle does it intersect?
a)
A) One
b)
B) Two
c)
C) Three
d)
D) Infinite
70.
If an inscribed angle measures 30°, what is the measure of the central angle subtending the same arc?
a)
A) 15°
b)
B) 30°
c)
C) 60°
d)
D) 90°
71.
If a radius is 5 cm and the tangent is drawn to a point on the circle, what is the distance from the center to the point of tangency?
a)
A) 10 cm
b)
B) 5 cm
c)
C) 7.5 cm
d)
D) 15 cm
72.
If two triangles have all three sides equal, what can you conclude?
a)
A) The triangles are similar.
b)
B) The triangles are congruent by SSS.
c)
C) The triangles can be either similar or congruent.
d)
D) The triangles are not related.
73.
Which statement is true about the relationships between angles in a circle?
a)
A) The central angle is always smaller than the inscribed angle.
b)
B) The inscribed angle is always larger than the central angle.
c)
C) The central angle is equal to twice the inscribed angle.
d)
D) The inscribed angle is equal to twice the central angle.
74.
What is the measure of an inscribed angle that intercepts a diameter?
a)
A) 0°
b)
B) 90°
c)
C) 180°
d)
D) 45°
75.
If a chord and a tangent intersect on a circle, what is the measure of the angle formed between them?
a)
A) Half the intercepted arc
b)
B) Double the intercepted arc
c)
C) Equal to the intercepted arc
d)
D) One-third the intercepted arc
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