Ten multiple-choice questions check the congruence criteria, corresponding parts, and rigid motions. Choose the single best answer for each question. The explanation after each question names the typical mistake.
GeometryCommon Core: G-CO.B.6 · G-CO.B.7 · G-CO.B.8 · G-SRT.B.5
🎯 Congruent Triangles: SSS, SAS, ASA, AAS and HL – Geometry math quiz
Question 1
Which criterion proves the two triangles congruent? Marked triangles.
A
SSS
B
ASA
C
SAS
D
HL
Question 2
\(\triangle ABC\cong\triangle DEF\). Which side corresponds to \(\overline{BC}\)?
A
\(\overline{DE}\)
B
\(\overline{DF}\)
C
\(\overline{AB}\)
D
\(\overline{EF}\)
Question 3
Which criterion proves the two right triangles congruent? Marked right triangles.
A
SAS
B
SSS
C
HL
D
AAS
Question 4
\(\triangle ABC\cong\triangle DEF\), \(m\angle A=(5x-8)^{\circ}\), and \(m\angle D=(3x+14)^{\circ}\). What is \(m\angle A\)?
A
\(11^{\circ}\)
B
\(55^{\circ}\)
C
\(47^{\circ}\)
D
\(33^{\circ}\)
Question 5
Two triangles each have two sides and a non-included angle congruent (SSA). Which statement is true?
A
They are always congruent by SAS.
B
They might not be congruent, because SSA can fit two triangles.
C
They are always congruent by ASA.
D
They are congruent only if they are acute.
Question 6
Two triangles both have angles of \(60^{\circ}\), \(60^{\circ}\), and \(60^{\circ}\). What can you conclude?
A
They have the same shape but may differ in size.
B
They are congruent by AAA.
C
They are congruent by AAS.
D
They have equal perimeters.
Question 7
\(\triangle PQR\cong\triangle STU\) by SAS. Which conclusion follows by CPCTC?
A
\(\angle Q\cong\angle T\)
B
\(\angle Q\cong\angle S\)
C
\(\angle Q\cong\angle U\)
D
\(\angle R\cong\angle T\)
Question 8
Triangle ABC is reflected across the \(y\)-axis. Where does the image of \(A(3,-2)\) land?
A
\((3,2)\)
B
\((-3,2)\)
C
\((2,-3)\)
D
\((-3,-2)\)
Question 9
Which criterion proves the two triangles congruent? Marked triangles.
A
ASA
B
AAS
C
SAS
D
SSS
Question 10
Two right triangles each have a hypotenuse of 10 and a leg of 6. How long is the other leg of each?
A
\(8\text{ units}\)
B
\(4\text{ units}\)
C
\(16\text{ units}\)
D
\(11.7\text{ units}\)
🎉 Quiz complete!
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Remember:
- Rigid motions keep lengths and angle measures, so an image triangle is congruent to the original.
- Valid criteria are SSS, SAS, ASA, AAS, and HL (right triangles only).
- SSA and AAA do not prove congruence.
- CPCTC: after triangles are proven congruent, all their corresponding parts are congruent.
See every chapter on the Geometry math page.