Triangles • Topic 2 of 5

Triangle Congruence

Two triangles are congruent when they are identical in shape and size — all corresponding sides and angles equal. You do not need to check all six parts; a few matching parts guarantee congruence. The standard criteria are SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the included side), and AAS (two angles and a non-included side). For right triangles there is also HL (hypotenuse-leg). Knowing which criterion applies lets you justify that two triangles are congruent from limited information. The SAT tests recognising the correct postulate from a description or diagram of equal parts.

Two congruent triangles with matching equal parts marked (SAS)Congruent triangles≅Same size and shape (SAS)

✅ Solved examples

1. Three sides of one triangle equal three sides of another. Which postulate?
SSS.
2. Two sides and the angle between them are equal. Which postulate?
SAS.
3. Two angles and the side between them are equal. Which postulate?
ASA.
4. What does it mean for two triangles to be congruent?
They have the same shape and size — all corresponding parts equal.

✏️ Practice — try these, take hints as needed

1. Two angles and a non-included side are equal. Which postulate?
Two angles, side not between.
—
—
AAS.
2. All three pairs of sides are equal. Which postulate?
Side-Side-Side.
—
—
SSS.
3. Two sides and the included angle are equal. Which postulate?
Side-Angle-Side.
—
—
SAS.
4. In congruent triangles, corresponding angles are:
Same size?
—
—
Equal.
5. Two angles and the included side equal. Which postulate?
Angle-Side-Angle.
—
—
ASA.

📝 Topic test — 8 questions

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