TRIANGLES
Introduction
This section of the chapter provides a detailed exploration of triangles, highlighting their crucial properties and congruence principles. A triangle,, identified as a closed figure formed by three intersecting lines, possesses three sides, three angles, and three vertices. The section also reflects on prior studies about properties of triangles and introduces new concepts pertaining to congruence.
Congruence of Triangles
Congruent figures share equal shape and size, applicable in everyday life; for example, congruent objects found in ice trays. Triangles are congruent if their corresponding sides and angles are equal. The relationship is symbolically expressed as ΞPQR β
ΞABC, where corresponding vertices match.
Criteria for Congruence
The section discusses four primary criteria for triangle congruence:
1. SAS (Side-Angle-Side): Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.
2. ASA (Angle-Side-Angle): Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding parts of another triangle.
3. AAS (Angle-Angle-Side): Two triangles are congruent if two angles and one non-included side are equal.
4. SSS (Side-Side-Side): Two triangles are congruent if all three sides of one triangle are equal to the corresponding sides of another triangle.
5. RHS (Right angle-Hypotenuse-Side): Applies specifically to right triangles where the hypotenuse and a side of one triangle are equal to the hypotenuse and a side of another triangle.
Additional Properties and Applications
The section covers important properties associated with isosceles triangles, particularly focusing on how angles opposite equal sides are also equal, supported by theorems and examples. Numerous exercises and applications reinforce these concepts, allowing for practical understanding of triangle properties.
Overall, the section serves as a comprehensive foundation for understanding the structure and congruence of triangles, crucial elements in geometry.