congruent figures: Figures that have the same shape and size. Corresponding sides and angles in congruent figures have the same measure. The symbol ≅ means congruent.

Are the parallelograms ABCD and LMNO congruent?

Step 1: Compare the corresponding angles and sides. The corresponding angles are in the same order in the names of the parallelograms.

Corresponding angles:

∠A ≅ ∠L: 135°
∠B ≅ ∠M: 45°
∠C ≅ ∠N: 135°
∠D ≅ ∠O: 45°

Corresponding sides:

AB ≅ LM: 6
BC ≅ MN: 4
CD ≅ NO: 6
DA ≅ OL: 4

Parallelograms ABCD and LMNO are congruent.

Test-Taking Hint

Make sure you answer the entire problem. If there are two questions, make sure you have two answers.

Definition

similar figures: Figures that have the same shape but do not need to be the same size. Corresponding angles of similar figures are congruent. The sides of similar figures are in proportion. The symbol ,means similar.

Determine Similarity

Are the triangles similar?

Step 1: Corresponding angles of similar figures are congruent. Are the angles congruent? Yes. Each triangle has angles that measure 31°, 37°, and 22°.

Step 2: Corresponding sides of similar figures are proportional, or have the same ratio. Write a ratio that compares each pair of corresponding sides. Reduce each ratio to lowest terms.

The corresponding sides all have the same ratio, 1 to 3. They are proportional.

Yes, the triangles are similar.

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Similarity and Congruence