Triangle Congruence Quiz
Questions: 16 · 10 minutes
1. In two triangles, two pairs of corresponding sides are equal. The angle between those two sides is also equal. Which congruence theorem applies?
AAS
SAS
SSS
SSA
2. Two right triangles have hypotenuses of equal length and one pair of corresponding legs of equal length. Which theorem directly establishes congruence?
HL
SSA
AAA
AAS only
3. Triangle PQR is reflected across a line to create triangle P′Q′R′. What conclusion follows from the reflection?
The triangles are congruent because a reflection preserves lengths and angle measures.
Only their areas are guaranteed to be equal.
The triangles are similar but may have different side lengths.
They are congruent only if the line of reflection passes through a vertex.
4. A diagonal AC divides quadrilateral ABCD into triangles ABC and CDA. Suppose AB = CD and BC = DA. What third fact allows an SSS congruence proof?
∠ABC = ∠CDA by the vertical angles theorem.
AC = AC by the reflexive property.
The diagonal bisects both angles automatically.
The quadrilateral has equal diagonals.
5. In two triangles, one pair of angles measures 45°, another corresponding pair measures 65°, and the side between those angles is equal in both triangles. Which theorem most directly proves congruence?
ASA
SAS
AAS
SSS
6. Triangle ABC has side lengths 4, 6, and 9. Triangle DEF also has corresponding side lengths 4, 6, and 9. Which theorem guarantees congruence?
AAA
SSS
ASA
HL
7. You know AB = DE and AC = DF. Which additional statement would let you prove △ABC ≅ △DEF by SAS?
∠B = ∠E
∠C = ∠F
∠A = ∠D
∠B = ∠F
8. Two triangles have corresponding side lengths of 7 and 10, plus equal angles opposite the sides of length 7. Why does this information not generally prove congruence?
Two sides can never be used in a congruence proof.
The information forms SSA, which can produce more than one possible triangle.
An angle can be used only when it is a right angle.
Congruence requires the triangles to have the same orientation.
9. Point M is the midpoint of both segments AB and CD. In triangles AMC and BMD, AM = BM and CM = DM. Which additional fact completes an SAS proof?
AC = BD because the triangles appear symmetric.
∠ACM = ∠DBM because M is a midpoint.
AB = CD because both segments contain midpoint M.
∠AMC = ∠BMD because they are vertical angles.
10. Which sequence consists entirely of transformations that preserve triangle congruence?
Dilation, translation, and reflection
Dilation, horizontal stretch, and reflection
Horizontal stretch, rotation, and translation
Rotation, reflection, and translation
11. Triangle ABC has coordinates A(0,0), B(4,0), and C(0,3). Triangle DEF has coordinates D(2,1), E(6,1), and F(2,4). What best establishes their congruence?
Both triangles have vertices in the same quadrants.
Their corresponding slopes are equal, which proves AAA congruence.
Both triangles include one horizontal side.
A translation by ⟨2,1⟩ maps A, B, and C to D, E, and F.
12. Two triangles each have angles measuring 40°, 60°, and 80°, but no side lengths are given. What can be concluded?
They are congruent by ASA.
They are congruent by AAA.
They are similar by AAA, but congruence is not guaranteed.
They cannot be similar because no sides are known.
13. If △ABC ≅ △DEF, which correspondence is indicated by the order of the letters?
A corresponds to F, B to E, and C to D.
A corresponds to D, B to F, and C to E.
A corresponds to E, B to D, and C to F.
A corresponds to D, B to E, and C to F.
14. What does it mean for two triangles to be congruent?
They have equal areas, even if their shapes differ.
Their corresponding angles are equal, but their side lengths may be proportional.
Their corresponding sides and corresponding angles have equal measures.
They have equal perimeters, even if their corresponding parts differ.
15. A proof has established that △JKL ≅ △MNP. Which statement can then be justified by CPCTC?
Side JK is congruent to side NP.
Every angle in △JKL equals every angle in △MNP.
∠K and ∠N are congruent.
The triangles must occupy the same position in the plane.
16. Two angles and the side between them in one triangle match the corresponding parts of another triangle. Which theorem proves the triangles congruent?
ASA
AAS
SAS
AAA