Definition of Congruent Triangles
Definition of Congruent Triangles is a key concept in Grade 7 math from Big Ideas Math Advanced 2, Chapter 2: Transformations. Students learn that two triangles are congruent if and only if they have the exact same size and shape, written as triangle ABC congruent to triangle DEF. Congruent figures are identical in every way except their position, meaning they can be moved, rotated, or reflected without changing their size or shape.
Key Concepts
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.
Common Questions
What does it mean for two triangles to be congruent?
Two triangles are congruent if they have the exact same size and the exact same shape. Every corresponding angle and side must be equal, though the triangles may be in different positions or orientations.
How do you write a congruence statement for triangles?
Use the symbol congruent to between the triangle names, such as triangle ABC congruent to triangle DEF, listing corresponding vertices in matching order.
Can congruent triangles be in different positions?
Yes. Congruent triangles can be moved, rotated, or flipped (reflected) without changing their congruence. Position in space does not affect whether two triangles are congruent.
How is congruence different from similarity?
Congruent figures are identical in both size and shape. Similar figures have the same shape but can be different sizes. Congruent figures are always similar, but similar figures are not always congruent.