4.2 Triangles and Their Properties

Exploring triangle classifications, angle sum properties, congruence, similarity, and special triangles.

本节包含的知识点

• 4.2.1 Triangle Classification — Classifying triangles by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).
• 4.2.2 Angle Sum and Properties — Understanding the triangle angle sum theorem (180°), exterior angles, and angle relationships in triangles.
• 4.2.3 Triangle Congruence — Proving triangles are congruent using criteria (SSS, SAS, ASA, AAS, HL) and applying congruence properties.
• 4.2.4 Triangle Similarity — Identifying similar triangles using similarity criteria (AA, SSS, SAS) and applying proportional relationships.
• 4.2.5 Special Triangles — Analyzing properties of special triangles including equilateral triangles and isosceles triangles with specific angle measures.
• 4.2.6 Triangle Inequality and Median/Altitude Properties — Applying triangle inequality theorem and understanding properties of medians, altitudes, and angle bisectors.