Properties and Criteria of Right Triangles
Grade 7 Geometry — Building on the Angle Sum Theorem
🔷 Introduction
In this lesson, we explore the special properties and criteria of right triangles. Everything we discover is built on one fundamental fact:
The sum of the angles in any triangle equals $180°$.
✅ Properties
Properties describe what is true IN a right triangle. If you already know a triangle is right, properties tell you additional facts about it.
🔍 Criteria
Criteria allow you to PROVE a triangle is right. If you don't know whether a triangle has a right angle, criteria help you determine it.
Property 1: Sum of Acute Angles
Statement: The sum of the two acute angles of a right triangle equals $90°$.
Explanation
- The sum of all angles in any triangle: $\angle A + \angle B + \angle C = 180°$
- In a right triangle, one angle (say $\angle A$) equals $90°$
- Therefore: $90° + \angle B + \angle C = 180°$
- So: $\angle B + \angle C = 180° - 90° = 90°$
Consequence: The two acute angles in a right triangle are complementary (they add up to $90°$).
Example
If one acute angle is $35°$, then the other acute angle is:
$90° - 35° = 55°$
Interactive visualization — available in the full lesson