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Congruent Triangles on the Coordinate Plane

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Congruent Triangles on the Coordinate Plane

Study Guide

SSS Congruence Theorem

The SSS Congruence Theorem states that if three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Important Notes

The congruence of triangles is not affected by rotations, translations, or reflections.
The distance formula is essential for determining the lengths of the sides of the triangles.
When two triangles are congruent, all corresponding sides and angles are equal.

Mathematical Notation

$\overline{AB}$ notation is used for line segments.

$\Delta ABC$ denotes a triangle with vertices A, B, and C.

$\cong$ denotes congruence.

Remember to use proper notation when proving the congruence of triangles in coordinate plane.

Why It Works

Isometry transformations preserve the shape and size of figures, hence, the congruence of triangles is preserved even if one is translated, rotated or reflected onto the other.

Remember

The distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ is used to find the lengths of the sides of the triangles.

Quick Reference

SSS Congruence:$\overline{AB} \cong \overline{DE}, \overline{BC} \cong \overline{EF}, \overline{AC} \cong \overline{DF} \rightarrow \Delta ABC \cong \Delta DEF$

Understanding Congruent Triangles on the Coordinate Plane

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

In the coordinate plane, we can use the distance formula to find the lengths of the sides of a triangle. If the lengths of the sides of two triangles are equal, then they are congruent.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Are the triangles with vertices A(1,2), B(3,4), C(2,3) and D(1,2), E(3,4), F(5,6) congruent?

Real-World Problem

Question Exercise

Intermediate

Sports Field Design

A sports field is designed in the shape of a triangle with vertices at coordinates A(2,3), B(5,7), C(1,4). Another field is planned with vertices at D(3,4), E(6,8), F(2,5). Are these fields going to be the same size and shape?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

What possible isometry transformations can map triangle ABC with vertices A(1,1), B(3,1), C(2,3) onto triangle DEF with vertices D(1,1), E(1,3), F(3,2)?

Challenge Quiz

Single Choice Quiz

Advanced

Are triangles with vertices A(1,2), B(3,4), C(2,3) and D(-1,-2), E(-3,-4), F(-2,-3) congruent?

Recap

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