Triangle Congruence Practice Worksheet

Practice identifying triangle congruence rules using SSS, SAS, ASA, AAS, and HL.

Try each problem on your own first. Then click Show solution to check the congruence rule and the reasoning behind it.

Triangle Congruence Rules

  • SSS: three pairs of congruent sides
  • SAS: two sides and the included angle
  • ASA: two angles and the included side
  • AAS: two angles and a non-included side
  • HL: hypotenuse and leg in right triangles
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Level 1: Identify the Congruence Rule

Problem 1

Two triangles have all three pairs of corresponding sides congruent. Which triangle congruence rule applies?

\[ AB \cong DE,\quad BC \cong EF,\quad AC \cong DF \]
Show solution

Three pairs of corresponding sides are congruent.

\[ \triangle ABC \cong \triangle DEF \quad \text{by SSS} \]
Problem 2

Two triangles have two pairs of corresponding sides congruent, and the angle between those sides is congruent. Which rule applies?

\[ AB \cong DE,\quad \angle B \cong \angle E,\quad BC \cong EF \]
Show solution

The angle is included between the two congruent sides.

\[ \triangle ABC \cong \triangle DEF \quad \text{by SAS} \]
Problem 3

Two triangles have two pairs of corresponding angles congruent, and the included side between those angles is congruent. Which rule applies?

\[ \angle A \cong \angle D,\quad AB \cong DE,\quad \angle B \cong \angle E \]
Show solution

The side is included between the two congruent angles.

\[ \triangle ABC \cong \triangle DEF \quad \text{by ASA} \]

Level 2: Included vs. Non-Included Parts

Problem 4

Two triangles have two pairs of corresponding angles congruent, and a side that is not between those angles is congruent. Which rule applies?

\[ \angle A \cong \angle D,\quad \angle C \cong \angle F,\quad AB \cong DE \]
Show solution

The given side is not included between the two angles.

\[ \triangle ABC \cong \triangle DEF \quad \text{by AAS} \]
Problem 5

Two right triangles have congruent hypotenuses and one pair of congruent legs. Which rule applies?

\[ \text{hypotenuse} \cong \text{hypotenuse} \] \[ \text{leg} \cong \text{leg} \]
Show solution

This rule only applies to right triangles.

\[ \triangle ABC \cong \triangle DEF \quad \text{by HL} \]
Problem 6

Two triangles have all three pairs of corresponding angles congruent. Does this prove the triangles are congruent?

\[ \angle A \cong \angle D,\quad \angle B \cong \angle E,\quad \angle C \cong \angle F \]
Show solution

No. AAA proves similarity, not congruence. The triangles may have the same shape but different sizes.

\[ \text{AAA does not prove triangle congruence.} \]

Level 3: Proof Reasoning

Problem 7

You are given:

\[ AB \cong DE,\quad BC \cong EF,\quad \angle B \cong \angle E \]

What congruence rule proves \(\triangle ABC \cong \triangle DEF\)?

Show solution

The congruent angle is between the two congruent sides.

\[ \triangle ABC \cong \triangle DEF \quad \text{by SAS} \]
Problem 8

You are given:

\[ \angle A \cong \angle D,\quad \angle B \cong \angle E,\quad AC \cong DF \]

What congruence rule proves \(\triangle ABC \cong \triangle DEF\)?

Show solution

The side \(AC\) is not the included side between \(\angle A\) and \(\angle B\). That makes this AAS.

\[ \triangle ABC \cong \triangle DEF \quad \text{by AAS} \]

Need more help with triangle congruence?

Triangle congruence becomes easier when students learn to identify which sides and angles correspond. For a full explanation, visit my Triangle Congruence guide.

Related Geometry Resources

Triangle Congruence Explained

Review SSS, SAS, ASA, AAS, HL, and congruence reasoning.

Geometry Proofs

Learn how triangle congruence connects to statements and reasons.

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