Angle Side Theorems Lesson 3.7.

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Presentation transcript:

Angle Side Theorems Lesson 3.7

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

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

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 <

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.

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

Rectangle: equiangular but not equilateral.

What are the restrictions on the values of 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?

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.