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Transcript
Lesson 4-4 Isosceles Triangle Theorem (page 134) Essential Question Can you construct a proof using congruent triangles? ISOSCELES TRIANGLE: a triangle with at least two sides congruent. congruent sides. LEGS (of an isosceles triangle): the _______________ third side. BASE (of an isosceles triangle): the __________ vertex angle: ∠A A vertex angle leg base angle B base angles: ∠B & ∠C leg base angle base C Theorem 4-1 The Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. A B Base angles of an isosceles triangle are congruent. C Given: Prove: A AB @ AC ∠B ∠C B Proof: Statements D Reasons C Corollary 1 An equilateral triangle is also equiangular . xº xº xº If all 3 sides are congruent, then all 3 angles are congruent. Corollary 2 An equilateral triangle has three 60 º 60 º 60 º 60º angles. Corollary 3 The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. Theorem 4-2 Converse of Theorem 4-1 If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Given: ∠B ∠C Prove: AB @ AC A B C Given: Prove: A ∠B ∠C AB @ AC Proof: B D C Corollary An equiangular triangle is also equilateral . xº xº xº If all 3 angles are congruent, then all 3 sides are congruent. Example # 1. Find the value of “x”. 40 º 3x-5 40º x + 21 3 x - 5 = x + 21 2 x - 5 = 21 2 x = 26 13 x = _____ Example # 2. Find the value of “x”. xº x + x + 70 = 180 70º xº 2 x = 110 55 x = _____ Example # 3. Find the value of “x”. 62º 62º xº xº 62 x = _____ Assignment Written Exercises on pages 137 to 139 RECOMMENDED: 1 to 7 odd numbers, 19 REQUIRED: 9, 14, 16, 22, 24, 27, 33 (use your template to draw the diagram for #33) Can you construct a proof using congruent triangles?