WorksheetsTRIANGLE CONGRUENCE TEST
Total questions: 20
Worksheet time: 10mins
Name
Class
Date
1.
What does CPCTC stand for, and how is it used in geometry?
a)
Congruent Points Create Triangle Congruence; it is used to prove that two triangles are congruent.
b)
Corresponding Parts of Congruent Triangles are Congruent; it is used to prove that specific parts (angles or sides) of two congruent triangles are also congruent.
c)
Corresponding Points of Congruent Triangles are Congruent; it is used before proving triangle congruence.
d)
Congruent Parts Create Triangle Congruence; it is used to match triangles with similar shapes.
2.
If △PQR is congruent to △STU, which of the following statements is false?
a)
∠P = ∠ S
b)
Side QR = Side TU
c)
Side PQ = Side ST
d)
∠R = ∠T
3.
If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, which postulate proves the triangles are congruent?
a)
ASA
b)
AAS
c)
SAS
d)
SSS
4.
In ΔABC and ΔDEF, AB ≅ DE, AC ≅ DF, and ∠A ≅ ∠D. What postulate can be used to prove ΔABC ≅ ΔDEF?
a)
AAS
b)
SAS
c)
ASA
d)
SSS
5.
Which of the following combinations cannot be used to prove triangles congruent?
a)
SAS
b)
ASA
c)
SSS
d)
SSA
6.
If ΔABC ≅ ΔDEF, which statement must be true?
a)
∠B ≅ ∠F only
b)
∠A ≅ ∠D and AB ≅ DE
c)
Only sides are congruent
d)
Angles are not congruent
7.
Which information is enough to prove ΔABC ≅ ΔDEF by SAS?
a)
Two sides and a non-included angle
b)
Two sides and the included angle
c)
Three angles
d)
Two angles and one side
8.
Given ΔABC with AB = 6 cm, BC = 8 cm, and ∠B = 45°, and ΔDEF with DE = 6 cm, EF = 8 cm, and ∠E = 45°, which triangles are congruent by which postulate?
a)
Yes, by SAS
b)
Yes, by ASA
c)
No, not enough information
d)
Yes, by AAS
9.
If two right triangles have hypotenuses and one leg congruent, they are congruent by which theorem?
a)
ASA
b)
AAS
c)
HL
d)
SAS
10.
Which condition is not necessary to use the HL Theorem?
a)
Both triangles are right triangles
b)
Hypotenuses are congruent
c)
One leg is congruent
d)
Both triangles are isosceles
11.
If ΔABC ≅ ΔXYZ by ASA, which parts must be congruent?
a)
Two sides only
b)
Two angles and the included side
c)
Three sides
d)
Two sides and non-included angle
12.
In a geometric proof, the statement CPCTC is most often used in which step, and why?
a)
At the beginning, to assume triangles are congruent and identify equal parts.
b)
After proving two triangles are congruent, to justify that specific sides or angles are congruent.
c)
In the middle, to substitute equal measures into equations before triangles are proven congruent.
d)
At the end, to determine that two triangles are similar, not congruent.
13.
If ΔABC ≅ ΔDEF by SAS, which pair represents the included angle?
a)
∠A and ∠D
b)
∠B and ∠E
c)
∠C and ∠F
d)
Any non-included angle
14.
Two triangles have all three corresponding sides congruent. What can you conclude?
a)
Triangles are congruent by SSS
b)
Triangles are congruent by ASA
c)
Triangles are similar only
d)
Triangles are not congruent
15.
A builder creates two triangular roof supports.
Each has sides of 4 ft, 6 ft, and 8 ft. However, one triangle faces left, and the other faces right.
What can be concluded about the two supports?
a)
They are not congruent because they are mirror images.
b)
They are congruent by SSS, since all three sides are equal in length.
c)
They are similar but not congruent, because they face opposite directions.
d)
They are congruent by ASA, since all sides are equal.
16.
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)
SSS (Side-Side-Side)
b)
SAS (Side-Angle-Side)
c)
ASA (Angle-Side-Angle)
d)
AAS (Angle-Angle-Side)
17.
Two triangles share one side. The remaining sides of both triangles are equal in length, and the included angles between those sides are congruent.
What can you conclude about the two triangles, and why?
a)
The triangles are congruent by SAS, because two sides and the included angle are congruent.
b)
The triangles are congruent by ASA, because they share one side and one angle.
c)
The triangles are similar, not congruent, because only the angles are the same.
d)
The triangles are not congruent because shared sides do not count in congruence.
18.
If ΔABC and ΔDEF are congruent, which of the following must also be congruent?
a)
∠A and ∠F
b)
BC and EF
c)
AC and EF
d)
∠C and ∠E only
19.
Two triangles are congruent by the SAS postulate. Which statement follows by CPCTC?
a)
Triangles have equal perimeters
b)
Their corresponding angles are equal
c)
Their areas are equal
d)
Their diagonals are equal
20.
Which congruence condition can be used to prove ∆ABC ≅ ∆XYZ?
a)
AA
b)
SSS
c)
SSA
d)
AAA
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