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Isosceles, Equilateral, and Right Triangles

Isosceles, Equilateral, and Right Triangles. Chapter 4.6. . Isosceles Triangle Theorem. Isosceles   The 2 Base s are  Base angles are the angles opposite the equal sides. B. A. C. If AB  BC, then A  C. Isosceles Triangle Theorem. B. A. C. If A  C then AB  BC.

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Isosceles, Equilateral, and Right Triangles

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  1. Isosceles, Equilateral, and Right Triangles Chapter 4.6

  2. Isosceles Triangle Theorem Isosceles   The 2 Base s are  • Base angles are the angles opposite the equal sides.

  3. B A C If AB  BC, then A  C Isosceles Triangle Theorem

  4. B A C If A  C then AB  BC Isosceles Triangle Theorem

  5. B A C Sample Problem Solve for the variables • mA = 32° • mB = (4y)° • mC = (6x +2)° 32 + 32 + 4y = 180 4y + 64 = 180 4y = 116 y = 29 6x + 2 = 32 6x = 30 x = 5

  6. Find the Measure of a Missing Angle 120o 30o 30o 75o 30o 75o 180o – 120o = 60o 180o – 30o = 150o Lesson 6 Ex2

  7. A • B • C • D A. 25 B. 35 C. 50 D. 130 Lesson 6 CYP2

  8. A. B. C. D. A. Which statement correctly names two congruent angles? • A • B • C • D Lesson 6 CYP3

  9. A. B. C. D. B. Which statement correctly names two congruent segments? • A • B • C • D Lesson 6 CYP3

  10. Equilateral Triangle Theorem Equilateral   Equiangular Each angle = 60o !!!

  11. Use Properties of Equilateral Triangles Linear pair Thm. Substitution Subtraction Answer: 105 Lesson 6 Ex4

  12. A • B • C • D A.x = 15 B.x = 30 C.x = 60 D.x = 90 Lesson 6 CYP4

  13. A • B • C • D A. 30 B. 60 C. 90 D. 120 Lesson 6 CYP4

  14. Don’t be an ASS!!! • Angle Side Side does not work!!! • (Neither does ASS backward!) • It can not distinguish between the two different triangles shown below. However, if the angle is a right angle, then they are no longer called sides. They are called…

  15. Hypotenuse-Leg   Theorem • If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts in another right triangle, then the triangles are congruent.

  16. Y B X Z A C ABC  XYZ Why?HL   Theorem

  17. Z X Y M Prove XMZ  YMZ Step Reason Given Given mZMX = mZMY = 90o Def of  lines Reflexive ZMX  ZMY HL   Thm

  18. AB  XY • BC  YZ • CA  ZX Corresponding Parts of Congruent Triangles are Congruent • Given ΔABC  ΔXYZ • You can state that: • A  X • B  Y • C  Z

  19. Suppose you know that ABD  CDB by SAS   Thm. Which additional pairs of sides and angles can be found congruent using Corr. Parts of  s are ?

  20. Complete the following two-column proof. Proof: Statements Reasons 1. Given 1. 2. 2. Isosceles Δ Theorem 3. 3. Given 4. 4. Def. of midpoint Lesson 6 CYP1

  21. Statements Reasons 4. 4. Def. of midpoint ? 5. ______ 6. 6. ? 5. ΔABCΔADC Complete the following two-column proof. • A • B • C • D Proof: SAS   Thm. Corr. Parts of s are  Lesson 6 CYP1

  22. Homework Video C Ch 4-6 • pg 248 1 – 10, 14 – 27, 32, 33, 37 – 39, & 48 Reminder! Midpoint Formula:

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