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4.5 Isosceles and Equilateral Triangles

4.5 Isosceles and Equilateral Triangles. Chapter 4 Congruent Triangles. 4.5 Isosceles and Equilateral Triangles. Isosceles Triangle:. Vertex Angle. Leg. Leg. Base Angles. Base. *The Base Angles are Congruent*. Isosceles Triangles. Theorem 4-3 Isosceles Triangle Theorem

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4.5 Isosceles and Equilateral Triangles

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  1. 4.5 Isosceles and Equilateral Triangles Chapter 4 Congruent Triangles

  2. 4.5 Isosceles and Equilateral Triangles Isosceles Triangle: Vertex Angle Leg Leg Base Angles Base *The Base Angles are Congruent*

  3. Isosceles Triangles • Theorem 4-3 Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent B <A = <C A C

  4. Isosceles Triangles • Theorem 4-4 Converse of the Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent B Given: <A = <C Conclude: AB = CB A C

  5. Isosceles Triangles • Theorem 4-5 The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base B Given: <ABD = <CBD Conclude: AD = DC and BD is ┴ to AC A C D

  6. Equilateral Triangles • Corollary: Statement that immediately follows a theorem Corollary to Theorem 4-3: If a triangle is equilateral, then the triangle is equiangular Corollary to Theorem 4-4: If a triangle is equiangular, then the triangle is equilateral

  7. Using Isosceles Triangle Theorems Explain why ΔRST is isosceles. T U Given: <R = <WVS, VW = SW Prove: ΔRST is isosceles R W V VW = SW Given S <V = <S Base angles are congruent in an isosceles triangle <V = <R Given <R = <S Transitive or Substitution Property If base angles are congruent, then the sides opposite them are congruent. RT = TS ΔRST is isosceles Two sides are congruent, definition of isosceles triangle

  8. Using Algebra Find the values of x and y: M ) ) y° Because <LMO = <NMO, MO is An angle bisector of isosceles triangle LMN. This makes it a perpendicular bisector, so x = N x° O 63° 90° L To solve for y: <N is 63° because it is an isosceles triangle. So… 27° 180 – 63 – 63 = 54° 54°/2 =

  9. Landscaping A landscaper uses rectangles and equilateral triangles for the path around the hexagonal garden. Find the value of x. (n – 2)180 (6 – 2)180 x° 4(180) 720 720/6 120 *60 + 90 + 90 + 120 = 360*

  10. Practice • Pg 213 1-16, 21-26

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