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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

4. Congruent Figures

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Exercise 13 Page 68

Use the symbol ≅ to name the corresponding sides and corresponding angles.

Corresponding Sides: AB ≅ EF, BC ≅ FG, CD ≅ GH, DA ≅ HE
Corresponding Angles: ∠ A ≅ ∠ E , ∠ B ≅ ∠ F, ∠ C ≅ ∠ G, ∠ D ≅ ∠ H

Practice makes perfect

We are given two congruent trapezoids.

Two congruent figures have the same size and the same shape. Also, their corresponding angles are congruent.

We can name the corresponding angles and the corresponding sides of the given trapezoids by using the symbol ≅, which means is congruent to. Let's start with the corresponding sides! AB ≅ EF BC ≅ FG CD ≅ GH DA ≅ HE Finally, we will name the corresponding angles. ∠ A ≅ ∠ E ∠ B ≅ ∠ F ∠ C ≅ ∠ G ∠ D ≅ ∠ H

Extra

Writing a Congruence Statement

As with polygons, when it comes to writing a triangle congruence statement, the order in which the vertices are written is critical. Naming them in an incorrect order leads to erroneous conclusions. Consider, for example, the following congruent triangles.

Although the triangles are congruent, the congruence statement △ ABC ≅ △ MQT is incorrect. Why? Because it would lead to the following conclusions about the sides and angles.

Always be sure to list the corresponding vertices in the correct order. Furthermore, another important concept to consider is that the claim that helps to determine whether two triangles are congruent is also valid for polygons. In fact, the claim is identical, except that triangles has been replaced by polygons.

Congruent Polygons
Two polygons are congruent if and only if their corresponding sides and angles are congruent.

Subchapter links

Try It p.64-65

Self-Assessment for Concepts & Skills p.65

Self-Assessment for Problem Solving p.66

Review & Refresh p.67

Concepts, Skills, & Problem Solving p.67-68