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Angle Side Theorems

Learn about Theorem 20 and 21 relating to sides and angles in triangles. Understand how to prove an isosceles triangle through congruent sides or angles. Discover the relationship between side lengths and angle measures in triangles, including cases of equilateral and equiangular properties. Practice solving triangle angle measures given specific conditions and restrictions on variable values.

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Angle Side Theorems

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  1. Angle Side Theorems Lesson 3.7

  2. Theorem 20: If two sides of a triangle are congruent, the angles opposite the sides are congruent. IF Then

  3. Theorem 21: If two angles of a triangle are congruent, the sides opposite the angles are congruent. If Then

  4. These are ways to prove an isosceles triangle: • Two sides are congruent. • Two angles are congruent. Markings on a triangle: Smaller side matches opposite < Medium side opposite med < Larger side opposite larger <

  5. Theorem: If two sides are not congruent, then the angles opposite are not congruent. Theorem: If two angles of a triangle are not congruent, their opposite sides are not congruent.

  6. Equilateral and Equiangular are interchangeable in triangles. Not in all shapes! Rhombus: equilateral but not equiangular.

  7. Rectangle: equiangular but not equilateral.

  8. A 6x-45 15+x B C Given: AC>AB m B + m C <180 m B = 6x – 45 m C = 15 + x What are the restrictions on the values of x?

  9. You must solve two unknowns. m B > m C 6x – 45 > 15 + x 5x > 60 x > 12 m B + m  C < 180 6x – 45 + 15 + x < 180 7x < 210 x < 30 Therefore, x must be between 12 and 30.

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