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Transcript
Isosceles Triangles & Corollaries Get: ♥ a piece of patty paper ♥ a straight edge ♥ your pencil ♥ your compass ♥ a protractor We are going to create an isosceles triangle with 2 congruent sides. Isosceles Triangles ♥ Has at least 2 congruent sides. ♥ The angles opposite the congruent sides are congruent ♥ Converse is also true. The sides opposite the congruent angles are also congruent. ♥ This is a COROLLARY. A corollary naturally follows a theorem or postulate. We can prove it if we need to, but it really makes a lot of sense. ♥ The bisector of the vertex angle of an isosceles Δ is the perpendicular bisector of the base. Vertex angle Base In addition, you just learned that the angles opposite congruent sides are congruent… Equilateral Triangle ♥ An Equilateral triangle is a special case of an Isosceles Triangle. ♥ Remember that an Isosceles Triangle has AT LEAST 2 congruent sides. ♥ An Equilateral Triangle is also Equiangular. ♥ The bisector of any angle is the perpendicular bisector of the opposite side. Let’s Practice Find the measures of: mFC = 4 mFG = 4 mCG = 4 m<C = 60◦ m<G = 60◦ m<F = 60◦ m<A = 70◦ m<E = 70◦ y= 50 ◦ Complete each statement. Explain why it is true. EAB ? BCD ? DBC FG ? DF Determine the measure of the indicated angle. ACB DCE BCD Find the value of x and y. An exterior angle of an isosceles triangle has a measure 140. Find two possible sets of measures for the angles of the triangle. Your assignment 4.5 Practice Worksheet