Lesson 1: Congruent Figures

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.

Property

Two segments are congruent if they have equal lengths: $\overline{AB} \cong \overline{CD}$ if and only if $AB = CD$. Congruent segments are marked with identical tick marks in geometric diagrams.

Examples

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: