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4.6 Congruence in Right Triangles

4.6 Congruence in Right Triangles. Chapter 4 Congruent Triangles. 4.6 Congruence in Right Triangles. Right Triangle. Hypotenuse. Leg. Leg. *The Hypotenuse is the longest side and is always across from the right angle*. Pythagorean Theorem. a 2 + b 2 = c 2. c.

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4.6 Congruence in Right Triangles

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  1. 4.6 Congruence in Right Triangles Chapter 4 Congruent Triangles

  2. 4.6 Congruence in Right Triangles Right Triangle Hypotenuse Leg Leg *The Hypotenuse is the longest side and is always across from the right angle*

  3. Pythagorean Theorem a2 + b2 = c2 c *c is always the hypotenuse a b

  4. Pythagorean Theorem a2 + b2 = c2 32 + 42 = c2 c *c is always the hypotenuse 9 + 16 = c2 3 25 = c2 c = 5 4

  5. Pythagorean Theorem a2 + b2 = c2 a2 + 52 = 132 13 *c is always the hypotenuse a2 + 25 = 169 a a2 = 144 a = 12 5

  6. Pythagorean Theorem 25 25 7 7 Are these triangles congruent?

  7. Congruence in Right Triangles Theorem 4-6 Hypotenuse-Leg (H-L) Theorem If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

  8. Congruence in Right Triangles Are the two triangles congruent? A X B C Y Z

  9. Proving Triangles Congruent Given: WJ = KZ, <W and <K are right angles Prove:ΔJWZ = ΔZKJ Z W J K WJ = KZ, <W and <K are right angles Given <W = <K All right angles are Congruent JZ = JZ Reflexive Property ΔJWZ = ΔZKJ H-L Theorem

  10. Proving Triangles Congruent Given: CD = EA, AD is the perpendicular bisector of CE Prove: ΔCBD = ΔEBA C D A B CD = EA, AD is the perpendicular bisector of CE Given E Definition of bisector CB = EB ΔCBD = ΔEBA H-L Theorem

  11. Practice • Pg 219 1-4 Write a two-column proof • Pg 219 5-8 Answer Question • Pg 220 9 - 10 Answer Question • Pg 220 11-12 Write a two-column proof • Pg 220-221 14-17 • Pg 222 28 – 29 Write a two-column proof

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