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Transcript
4-5 Isosceles and Equilateral Triangles Objective SWBAT use and apply properties of isosceles and equilateral triangles. Important Info What do you know about isosceles and equilateral triangles? These are the triangles we frequently see out in the real world. In bridges, structures, art, etc. Isosceles Triangles • The congruent sides of an isosceles triangle are its _________. The third side is its _________. The two congruent legs form the ___________________. The other two angles are the ______________________. Theorem 4-3 Isosceles Triangle Theorem If two _________ of a triangle are _______, then the angles ______________ those sides are _________. Theorem 4-4 Converse of the Isosceles Triangle Theorem You tell me, what is the converse of the Isosceles Triangle Theorem? ___________________________________________________________ ___________________________________________________________. Example 1 Using the Isosceles Triangle Theorems B A) Is AB congruent to CB? Explain. B) Is <A congruent to <DEA? Explain. D C A E A) Is <WVS congruent to <S? Is TR congruent to TS? Explain. B) Can you conclude that triangle RUV is isosceles? Explain. T U W R S V Theorem 4-5 Isosceles Bisector Theorem If a line bisects the _________________ of an isosceles triangle, then the line is also the ____________________ of the base. B Example 2 Using Algebra What is the value of x? What if <A = 27? X 54 A C D • A ________________ is a theorem that can be proved easily using another _______________. Because of this, you can use it as a reason in a proof. Corollary to Theorem 4-3 If a triangle is __________________, then the triangle is ________________. Corollary to Theorem 4-4 If a triangle is __________________, then the triangle is ________________. Example 3 Finding Angle Measures D C What is the measures of <A, <B, and <ADC? A B E Suppose the triangle are isosceles, where <ADE, <DEC, and <ECB are vertex angles. If the vertex angle each have a measure of 58, what are m<A, and m<BCD? Homework ____________________________
