Triangles - Advanced Pages

Aug 31, 2026

Uploaded by Aurelia

Advanced study notes on triangles, covering key triangle types (scalene, isosceles, equilateral, and isosceles right-angled) with defining properties and angle-side relationships. Fundamental triangle properties summarize inequality relations among sides, angle-sum rules for interior angles and exterior angles, and classifications of acute, right, and obtuse triangles using the c² comparison to a²+b². The document further explains congruence criteria (SSS, SAS, ASA, AAS, and RHS) and similarity theorems for similar triangles (AAA, SSS, and SAS).

LanguageEnglish

CategoryExam

FormatPDF

Pages17

Reading Time43 min

AccessFree to download

Triangles

Types of triangles

Fundamental properties of triangles

Congruence of triangles

Theorems related to similar triangles

Important Definition

FAQs

What are the main types of triangles and their defining conditions?

The notes distinguish scalene, isosceles, equilateral, and isosceles right-angled triangles, using which sides are equal and how the angles relate (e.g., equilateral angles are 60°).

How are acute, right, and obtuse triangles identified using side lengths?

Let c be the largest side. If c² < a²+b² the triangle is acute; if c² = a²+b² it is right-angled; if c² > a²+b² it is obtuse.

What congruence tests are listed for proving two triangles congruent?

The document lists SSS, SAS, ASA (A-S-A), AAS (Angle-Angle-Side), and RHS (Right angle-Hypotenuse-Side) as congruence criteria.

Aug 31, 2026

Uploaded by Aurelia