Little Learnersplay. practice. discover.
Explore

Grade 10 · Math

Choose evidence for triangle congruence

Distinguish valid triangle-congruence conditions from insufficient evidence.

6 authored questions + worked example

Play this skill Make a practice check

Worked example

All three pairs of corresponding sides have equal lengths.

Answer & why

Answer: SSS

Three corresponding side equalities establish side-side-side congruence.

Add to plan

All questions

All 6 authored questions for this skill.

Question 1

Two pairs of corresponding angles and their included sides are equal.

  1. AAA
  2. SAS
  3. ASA
  4. SSS
A hint

Check exactly which sides and angles are given, including whether the angle or side is included.

Answer & why

Answer: ASA

The matched side lies between the matched angles, so angle-side-angle applies.

Add to plan

Question 2

Two pairs of corresponding angles and a nonincluded pair of sides are equal.

  1. SAS
  2. AAS
  3. AAA
  4. SSS
A hint

Check exactly which sides and angles are given, including whether the angle or side is included.

Answer & why

Answer: AAS

Two angles determine the third; a matched nonincluded side fixes the size.

Add to plan

Question 3

Only all three corresponding angle pairs are known equal. Is congruence guaranteed?

  1. Yes, by SAS.
  2. No; the triangles may have different sizes.
  3. Yes, by ASA.
  4. Yes, by SSS.
A hint

Check exactly which sides and angles are given, including whether the angle or side is included.

Answer & why

Answer: No; the triangles may have different sizes.

Equal angles guarantee similarity, but a larger scaled copy has the same angles and different side lengths.

Add to plan

Question 4

Only two corresponding side pairs and a nonincluded angle are known equal in arbitrary triangles. Is congruence always guaranteed?

  1. Yes, by ASA.
  2. Yes, by SSS.
  3. Yes, by SAS.
  4. No; SSA does not always fix a unique triangle.
A hint

Check exactly which sides and angles are given, including whether the angle or side is included.

Answer & why

Answer: No; SSA does not always fix a unique triangle.

The angle is not between the matched sides; this SSA information can allow two different triangles.

Add to plan

Question 5

All three pairs of corresponding sides have equal lengths.

  1. AAA
  2. SSS
  3. ASA
  4. SAS
A hint

Check exactly which sides and angles are given, including whether the angle or side is included.

Answer & why

Answer: SSS

Three corresponding side equalities establish side-side-side congruence.

Add to plan

Question 6

Two pairs of corresponding sides and their included angles are equal.

  1. AAA
  2. SSS
  3. AAS
  4. SAS
A hint

Check exactly which sides and angles are given, including whether the angle or side is included.

Answer & why

Answer: SAS

The angle lies between the two matched sides, which gives side-angle-side.

Add to plan