Chapter 1
Number and Quantity
Course: Core Academic Skills For Educators Combined Test 5752
Subject: Core Academic Skills Educators Mathematics 5733
Chapter: Geometry
Congruency and similarity are two related but distinct concepts in geometry that allow us to determine relationships between shapes, compare their properties, and solve both theoretical and applied problems. They provide essential tools for analyzing structures, scaling objects, and proving geometric results.
Congruent figures
Congruent figures have exactly the same size and shape. This means that all corresponding sides are equal in length and all corresponding angles are equal in measure. To move one congruent figure onto another, only rigid transformations are needed: translation (sliding), rotation (turning), or reflection (flipping).
Key properties of congruence:
- Corresponding angles are equal.
- Corresponding sides are equal.
- The figures overlap perfectly when superimposed.
Congruence criteria for triangles (most commonly tested):
- Side-Side-Side (SSS): If three sides of one triangle equal the three sides of another.
- Side-Angle-Side (SAS): If two sides and the included angle match.
- Angle-Side-Angle (ASA): If two angles and the included side match.
- Angle-Angle-Side (AAS): If two angles and a non-included side match.
- Hypotenuse-Leg (HL): In right triangles, if the hypotenuse and one leg match.