A triangle with two equal sides is called an isosceles triangle. The two equal sides are called the legs, the remaining side is called the base, the angles at the ends of the base are called the base angles, and the angle at the vertex is called the vertex angle.
Properties of Isosceles Triangles
- The base angles are equal (∠B = ∠C)
- The bisector of the vertex angle bisects the base at a right angle
Example ①
In △ABC, when AB=AC and ∠A=40°, find ∠B and ∠C.
Answer: ∠B=∠C (base angles). ∠B+∠C=180°−40°=140°. ∠B=∠C=70°
In △ABC, when AB=AC and ∠A=40°, find ∠B and ∠C.
Answer: ∠B=∠C (base angles). ∠B+∠C=180°−40°=140°. ∠B=∠C=70°
Key Points
- AB=AC → ∠B=∠C (the base angles are equal)
- ∠A+2∠B=180°
Practice Problems
- In △ABC, when AB=AC and ∠B=65°, find ∠A.
- In △ABC, when AB=AC and ∠A=100°, find ∠B.
Answers and Explanations
- Answer: ∠A=50°. ∠C=65° (base angles). ∠A=180−65−65=50.
- Answer: ∠B=40°. ∠B=(180−100)/2=40.