Congruent triangles are commonly used in the construction of bridges, buildings, and quilts. Congruent triangles are also used to calculate inaccessible distances, such as the width of a river or the distance to the sun. You will learn simple ways to make sure that two triangles are congruent.
These teaching notes can be printed for quick referencing.
In this chapter students will:
- build on their knowledge of triangles
- learn to prove two triangles congruent by the SSS Postulate, SAS Postulate, ASA Postulate, AAS Theorem, and the HL Theorem
- learn to use triangle congruence and CPCTC to prove that parts of two triangles are congruent
- learn to identify congruent overlapping triangles
- prove two triangles congruent by first proving two other triangles congruent
- learn to apply these concepts to indirect measurement
- learn how these concepts are applied in engineering and construction
Prerequisite Skills
- understand congruence
- construct angles and segments
- write proofs
- understand the SSS, ASA, and SAS Postulates and the AAS Theorem
- apply the SSS, ASA, and SAS Postulates and the AAS and HL Theorems
Key Terms
- Angle-Angle-Side Theorem
- Angle-Side-Angle Postulate
- CPCTC (corresponding parts of congruent triangles are congruent)
- Hypotenuse-Leg Theorem
- quadratic formula
- Side-Angle-Side Postulate
- Side-Side-Side Postulate
- standard form of a quadratic equation