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Overview
Mathematics 11
Geometry
4. Derive proofs involving properties of angles and triangles
4.2 Isosceles and equilateral triangles
Isosceles and Equilateral Triangles
Discover how equal sides create equal angles in isosceles and equilateral triangles, and learn to solve for missing angles, sides, and area.
What You'll Learn
Identify an isosceles triangle by its two equal sides and an equilateral triangle by all three equal sides
Apply the base angles theorem to show that angles opposite equal sides are always equal
Recognize that every equilateral triangle is isosceles and has three sixty degree angles
Classify isosceles triangles as acute, right, or obtuse based on the vertex angle
Calculate the area of an isosceles triangle by finding its height then using one half base times height
Solve for unknown sides or angles using the triangle angle sum and the base angles theorem together
What You'll Practice
1
Finding missing angles in equilateral triangles
2
Solving for variables using equal side lengths in isosceles triangles
3
Determining unknown angles using the 180-degree triangle sum
4
Proving triangles are isosceles using congruence theorems
Why This Matters
Mastering isosceles and equilateral triangles builds your foundation for geometry proofs, trigonometry, and real-world applications like engineering and architecture. These special triangles appear throughout higher math, and recognizing their properties helps you solve complex problems quickly.
This Unit Includes
5 Video lessons
Learning resources
Skills
Isosceles Triangles
Equilateral Triangles
Triangle Sum Theorem
Congruence
Angle Properties
Algebraic Reasoning
Geometric Proofs
NS Curriculum Aligned