SAT MathGeometry & Trigonometry5 Practice Questions

Triangle Congruence and Similarity — SAT Math Explained

Congruent triangles have identical shape and size (all corresponding angles and sides are equal). Similar triangles have identical shape but different sizes (corresponding angles are equal, corresponding sides are proportional).

Core Idea Common Errors Practice Questions ↓

The Core Idea

You don't need all 6 measurements (3 sides and 3 angles) to prove triangles are congruent or similar — certain combinations are sufficient. These shortcuts allow powerful geometric proofs.

Congruence Postulates

SSS

Side-Side-Side — all three pairs of corresponding sides are equal

SAS

Side-Angle-Side — two sides and the included angle are equal

ASA

Angle-Side-Angle — two angles and the included side are equal

AAS

Angle-Angle-Side — two angles and a non-included side are equal

Hypotenuse-Leg — for right triangles only

Similarity Postulates

Angle-Angle — two pairs of corresponding angles are equal (most common)

SSS (Similarity)

All three pairs of corresponding sides are proportional

SAS (Similarity)

Two sides proportional and the included angle equal

Using Similarity

Set up proportions between corresponding sides: a/d = b/e = c/f

Solve for the unknown side using cross-multiplication

Verify the scale factor is consistent across all sides

Real World Application

Measuring the height of a tall object using its shadow and a known reference object (shadow method relies on similar triangles)

Common Errors to Avoid

Using SSA to prove congruence — SSA is NOT a valid congruence postulate (ambiguous case)

Setting up proportions with non-corresponding sides (must match corresponding vertices)

Confusing congruence (=) with similarity (∼)

Practice: Triangle Congruence and Similarity

5 SAT-style questions. Select your answer and get an instant explanation.

5 Q's

Question 1 of 5Easy

Which is a valid triangle congruence shortcut?

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SAT Triangle Congruence and Similarity Practice Questions

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Triangle Congruence and Similarity Full Practice Test

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All Topics in Geometry & Trigonometry

Lines and Angles Triangle Properties Triangle Congruence and Similarity Circle Properties Area and Circumference Arc Length and Sectors Area of Shapes Volume of 3D Shapes Distance Formula Midpoint Formula Equation of a Line Basic Trigonometry (sin, cos, tan)Right Triangle Problems Angles in Degrees