Geometry Triangles & Congruence 2 — Questions and Answers
Question 1: Two triangles have all three pairs of corresponding sides equal in length. Which congruence postulate proves them congruent?
- SSS (Correct answer)
- AAA
- SSA
- ASA
Correct answer: SSS
Three pairs of equal sides guarantee congruence by the Side-Side-Side postulate.
Question 2: Which combination does NOT guarantee two triangles are congruent?
- SSA (Correct answer)
- SAS
- ASA
- AAS
Correct answer: SSA
SSA (Side-Side-Angle) is ambiguous and does not guarantee congruence.
Question 3: In triangle ABC, angle A = 50 degrees and angle B = 60 degrees. What is angle C?
- 70 degrees (Correct answer)
- 80 degrees
- 60 degrees
- 90 degrees
Correct answer: 70 degrees
Angles of a triangle sum to 180, so C = 180 - 50 - 60 = 70.
Question 4: The Hypotenuse-Leg (HL) theorem applies only to which type of triangle?
- Right triangles (Correct answer)
- Equilateral triangles
- Obtuse triangles
- Scalene triangles
Correct answer: Right triangles
HL congruence is valid only for right triangles because it references the hypotenuse.
Question 5: Two triangles have two pairs of equal angles and the included sides equal. Which postulate applies?
- ASA (Correct answer)
- SSS
- SAS
- HL
Correct answer: ASA
Two angles with the side between them equal proves congruence by Angle-Side-Angle.
Question 6: If two triangles are congruent, what is true about their corresponding parts?
- All corresponding sides and angles are equal (Correct answer)
- Only the sides are equal
- Only the angles are equal
- Only the perimeters are equal
Correct answer: All corresponding sides and angles are equal
Congruent triangles have all corresponding sides and angles equal (CPCTC).
Question 7: A triangle has sides 5, 5, and 8. What type of triangle is it by its sides?
- Isosceles (Correct answer)
- Equilateral
- Scalene
- Right
Correct answer: Isosceles
Exactly two equal sides make the triangle isosceles.
Geometry Triangles & Congruence 2
Two triangles have all three pairs of corresponding sides equal in length.
Which congruence postulate proves them congruent?