知识点 3

Use properties of isosceles and equilateral triangles.

Use the equal base angles of isosceles triangles and the 60° angles of equilateral triangles.

核心知识

In an isosceles triangle, the two base angles are equal. In an equilateral triangle, all three angles are 60° and all three sides are equal.

深入理解

Rule: In an isosceles triangle, the angles opposite the equal sides are equal.

  • The vertex angle is the angle between the equal sides.
  • The two base angles are equal.
  • In an equilateral triangle, all angles are 60∘.

If you know one angle, the other two usually come from 180∘ minus that angle.

分步讲解

  1. Identify which sides are equal — the angles opposite those sides are the base angles.
  2. If the vertex angle is known, compute each base angle as 180°−vertex2.
  3. If a base angle is known, compute the vertex angle as 180 ° −2 ×base angle.
  4. For equilateral triangles, all angles are 60° and all sides are equal — use this directly.

常见误解

  • Assuming the "base" must be the bottom side — the base is whichever side is opposite the vertex angle.
  • Forgetting that an equilateral triangle is also isosceles.
  • Setting up the equation as 180 =𝑥 +𝑥 instead of 180 =𝑥 +𝑥 +vertex angle.
题目

示例解析

In an isosceles triangle, the vertex angle measures 50 °. What is the measure of each base angle?

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