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Warm Up 1. Write a congruence statement for the triangles.

K. A. Warm Up 1. Write a congruence statement for the triangles. 2 . Which Congruence Theorem supports your conclusion? 3. Which of the following statements is true by CPCTC? C  K . J. L. C. B. ABCLKJ.

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Warm Up 1. Write a congruence statement for the triangles.

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  1. K A • Warm Up • 1. Write a congruence statement for the triangles. • 2.Which Congruence Theorem supports your conclusion? • 3.Which of the following statements is true by CPCTC? C  K J L C B ABCLKJ SSA. There are 2 congruent sides and 1 angle. The angle is not between the sides.

  2. 4.5 Isosceles and Equilateral Triangles Target: SWBAT use and apply properties of isosceles and equilateral triangles.

  3. Vocabulary Isosceles triangle legs of an isosceles triangle vertex angle base base angles Equilateral and Equiangular triangles

  4. Recall that an isosceles triangle has at least two congruent sides. The congruent sides are called the legs. The vertex angle is the angle formed by the legs. The side opposite the vertex angle is called the base, and the base angles are the two angles that are connected by the base. A 3 is the vertex angle. 1 and 2are the base angles. Sides are the legs Side is the base B C

  5. 4-3 Pg 250 4-4 Pg 251

  6. - Page 252

  7. A corollary is a theorem that can be proved easily using another theorem. Page 252 Corollary to Theorem 4-3

  8. Page 252 Corollary to Theorem 4-4

  9. Assignment #38: Pages 254-256 Foundation: 10-13 Core: 14, 16-19, 22, 28, 30-31 Challenge: 32

  10. Example 2A: Finding the Measure of an Angle Find mF. mF= mD = x° Isosc. ∆ Thm. mF+ mD + mA = 180 ∆ Sum Thm. Substitute the given values. x+ x + 22 = 180 Simplify and subtract 22 from both sides. 2x= 158 Divide both sides by 2. x= 79 Thus mF = 79°

  11. Example 2B: Finding the Measure of an Angle Find mG. mJ= mG Isosc. ∆ Thm. Substitute the given values. (x+ 44) = 3x Simplify x from both sides. 44= 2x Divide both sides by 2. x= 22 Thus mG = 22° + 44° = 66°.

  12. Check It Out! Example 2A Find mH. mH= mG = x° Isosc. ∆ Thm. mH+ mG + mF = 180 ∆ Sum Thm. Substitute the given values. x+ x + 48 = 180 Simplify and subtract 48 from both sides. 2x= 132 Divide both sides by 2. x= 66 Thus mH = 66°

  13. Check It Out! Example 2B Find mN. mP= mN Isosc. ∆ Thm. Substitute the given values. (8y – 16) = 6y Subtract 6y and add 16 to both sides. 2y= 16 Divide both sides by 2. y= 8 Thus mN = 6(8) =48°.

  14. Example 3A: Using Properties of Equilateral Triangles Find the value of x. ∆LKM is equilateral. Equilateral ∆  equiangular ∆ The measure of each  of an equiangular ∆ is 60°. (2x + 32) = 60 Subtract 32 both sides. 2x= 28 Divide both sides by 2. x= 14

  15. Example 3B: Using Properties of Equilateral Triangles Find the value of y. ∆NPO is equiangular. Equiangular ∆  equilateral ∆ Definition of equilateral ∆. 5y – 6 = 4y + 12 Subtract 4y and add 6 to both sides. y= 18

  16. Check It Out! Example 3 Find the value of JL. ∆JKL is equiangular. Equiangular ∆  equilateral ∆ Definition of equilateral ∆. 4t – 8 = 2t + 1 Subtract 4y and add 6 to both sides. 2t= 9 t= 4.5 Divide both sides by 2. Thus JL= 2(4.5) + 1 =10.

  17. Lesson Quiz: Part I Find each angle measure. 1. mR 2. mP Find each value. 3.x 4.y 5.x 28° 124° 6 20 26°

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