Understanding Congruent Triangles
Congruent triangles are triangles that are identical in shape and size. They can be superimposed on one another, meaning all corresponding sides and angles are equal.
Congruence Rule
The congruence rule that applies to the given pair of congruent triangles can be one of the following:
- SSS (Side-Side-Side): All three sides of one triangle are equal to the three sides of another triangle.
- SAS (Side-Angle-Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
- ASA (Angle-Side-Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
- AAS (Angle-Angle-Side): Two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.
- RHS (Right Angle-Hypotenuse-Side): In right-angled triangles, if the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of another triangle, they are congruent.
Corresponding Parts of Congruent Triangles
When two triangles are congruent, the following corresponding parts are equal:
- Corresponding Sides:
- If triangle ABC is congruent to triangle DEF, then:
- AB = DE
- BC = EF
- CA = FD
- Corresponding Angles:
- Similarly, the angles are also equal:
- Angle A = Angle D
- Angle B = Angle E
- Angle C = Angle F
Conclusion
Understanding the congruence rules and corresponding parts is essential in geometry. It helps in solving various geometric problems and proofs effectively.