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"Congruent" Explained

Same sides and angles. Nneed to know if all angles are the same and at least one side on each is the same.

Key Idea: Congruent

Congruent figures have exactly the same size and shape — meaning all corresponding sides and angles are equal.

General Rule:

  • All corresponding angles must be equal.

  • All corresponding sides must be equal.

  • Congruence can be proven using criteria like SSS, SAS, ASA, AAS, or HL for triangles.

Why this matters for the SAT:

Congruence is often tested in geometry problems involving triangles and transformations. Recognizing when figures are congruent lets you transfer side lengths and angle measures between them to solve quickly.

"Corresponding Sides" Explained

These sides are connected.

Key Idea: Corresponding Sides

Corresponding sides are the matching sides of two figures that occupy the same relative position in each shape.

General Rule:

  • Corresponding sides are paired between figures (often in similar or congruent shapes).

  • Their positions match based on how the shapes are labeled or oriented.

  • In similar figures, corresponding sides are proportional.

  • In congruent figures, corresponding sides are equal.

Why this matters for the SAT:

Identifying corresponding sides is essential for setting up correct proportions, proving similarity or congruence, and solving for unknown lengths in geometry problems. Misidentifying them is a common SAT trap.

"Similar" Explained

Two triangles have the same angles but maybe not the same side lengths. But the trig ratios or side ratios are the same.

Key Idea: Similar Triangles

Two triangles are similar if they have the same angles.
Their side lengths may differ, but the ratios of corresponding sides are equal.

General Rule:

  • Corresponding angles are congruent.

  • Corresponding sides are in proportion:

Side 1 of Triangle A / Side 1 of Triangle B = Side 2 of Triangle A / Side 2 of Triangle B

  • Trigonometric ratios for corresponding angles are the same.

Why this matters for the SAT:

Recognizing similar triangles helps solve geometry and trigonometry problems.
It allows you to use proportions or trig ratios to find missing side lengths or angles efficiently.