Learn on PengiBig Ideas Math, Course 3Chapter 2: Transformations

Lesson 1: Congruent Figures

In this Grade 8 lesson from Big Ideas Math, Course 3 (Chapter 2: Transformations), students learn to identify congruent figures by determining whether corresponding angles and corresponding sides are congruent. Using geoboards and geometric diagrams, students practice naming corresponding parts of congruent polygons and applying the congruence symbol (≅) to express relationships between figures such as triangles and trapezoids. The lesson prepares students for Common Core Standard 8.G.2 by building foundational skills in recognizing and working with congruent figures.

Section 1

Definition of Congruent Triangles

Property

Two figures are congruent if and only if they have the exact same size and the exact same shape. We write $\Delta ABC \cong \Delta DEF$ to show that triangle $ABC$ is congruent to triangle $DEF$ .

Examples

Two squares with side length 5 cm are congruent because they have identical size and shape.
A triangle with sides 3 cm, 4 cm, and 5 cm is congruent to another triangle with the exact same side lengths, even if one is rotated or flipped.
Two rectangles with dimensions 6 cm by 8 cm are congruent, regardless of their position or orientation on a page.

Explanation

Congruent figures are identical in every way except for their position in space. Think of congruent figures as exact clones of each other that can be moved around, flipped over, or turned without changing their inherent size or shape. When figures are congruent, every corresponding angle and side must be completely equal.

Section 2

Identifying Corresponding Parts and Writing Congruence Statements

Property

In congruent figures, corresponding parts are the matching angles and sides that occupy the same relative positions.

A congruence statement ( $\Delta ABC \cong \Delta DEF$ ) is valid if and only if the vertex order perfectly reflects the actual correspondence:

A \leftrightarrow D, \quad B \leftrightarrow E, \quad C \leftrightarrow F

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Definition of Congruent Triangles

Property

Two figures are congruent if and only if they have the exact same size and the exact same shape. We write $\Delta ABC \cong \Delta DEF$ to show that triangle $ABC$ is congruent to triangle $DEF$ .

Examples

Two squares with side length 5 cm are congruent because they have identical size and shape.
A triangle with sides 3 cm, 4 cm, and 5 cm is congruent to another triangle with the exact same side lengths, even if one is rotated or flipped.
Two rectangles with dimensions 6 cm by 8 cm are congruent, regardless of their position or orientation on a page.

Explanation

Section 2

Identifying Corresponding Parts and Writing Congruence Statements

Property

In congruent figures, corresponding parts are the matching angles and sides that occupy the same relative positions.

A congruence statement ( $\Delta ABC \cong \Delta DEF$ ) is valid if and only if the vertex order perfectly reflects the actual correspondence:

A \leftrightarrow D, \quad B \leftrightarrow E, \quad C \leftrightarrow F

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Definition of Congruent Triangles

Property

Two figures are congruent if and only if they have the exact same size and the exact same shape. We write $\Delta ABC \cong \Delta DEF$ to show that triangle $ABC$ is congruent to triangle $DEF$ .

Examples

Two squares with side length 5 cm are congruent because they have identical size and shape.
A triangle with sides 3 cm, 4 cm, and 5 cm is congruent to another triangle with the exact same side lengths, even if one is rotated or flipped.
Two rectangles with dimensions 6 cm by 8 cm are congruent, regardless of their position or orientation on a page.

Explanation

Section 2

Identifying Corresponding Parts and Writing Congruence Statements

Property

In congruent figures, corresponding parts are the matching angles and sides that occupy the same relative positions.

A congruence statement ( $\Delta ABC \cong \Delta DEF$ ) is valid if and only if the vertex order perfectly reflects the actual correspondence:

A \leftrightarrow D, \quad B \leftrightarrow E, \quad C \leftrightarrow F