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Aim: How to prove triangles are congruent using a 5 th shortcut: Hyp-Leg.

Aim: How to prove triangles are congruent using a 5 th shortcut: Hyp-Leg. Pythagorean Theorem. a. c. a 2 + b 2 = c 2. b. Do Now:. In a right triangle, the length of the hypotenuse is 20 and the length of one leg is 16. Find the length of the other leg. 20. x. 12.

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Aim: How to prove triangles are congruent using a 5 th shortcut: Hyp-Leg.

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  1. Aim: How to prove triangles are congruent using a 5th shortcut: Hyp-Leg. Pythagorean Theorem a c a2 + b2 = c2 b Do Now: In a right triangle, the length of the hypotenuse is 20 and the length of one leg is 16. Find the length of the other leg. 20 x 12 x2 + 162 = 202 16 x2 + 256 = 400 x2 = 144 x = 12

  2. Hypotenuse-Leg V.HYP-LEG DABC and DA’B’C’ are right triangles A A’ B C B’ C’ If hypotenuse AC  hypotenuse A’C’, and leg BC  leg B’C’ then right DABC  right DA’B’C’ If the Hyp-Leg  Hyp-Leg, then the right triangles are congruent

  3. Model Problem ABC, BD  AC, AB  CB. Explain why ADB  CDB. DABC and DCBD are right triangles – BD  AC and form right angles, Triangles with right angles are right triangles. AB  BC – We are told so, and both AB & BC are hypotenuses (of DABD & DBDC respectively) Hyp  Hyp BD  BD – Anything is equal to itself; BD is a leg for both right triangles - Reflexive Leg  Leg ADB  CDBbecause of Hyp - Leg  Hyp - Leg

  4. Model Problem ABD is right, CDB is right, AD  CB. Explain why ADB  CDB. DABD and DCBD are right triangles – Triangles with right angles are right triangles. AD  CB – We are told so, and both AC & BD are hypotenuses (of DBCA & DCBD respectively) Hyp  Hyp BD  BD – Anything is equal to itself; BD is a leg for both right triangles - Reflexive Leg  Leg ADB  CDBbecause of Hyp - Leg  Hyp - Leg

  5. Model Problem PB  AC, PD  AE, AB  AD. Explain why ABP ADP DADP and DABP are right triangles – PB  AC and PD  AE and form right angles, Triangles with right angles are right triangles. AB  AD – We are told so, and each is a leg of their respective triangles. Leg  Leg AP  AP – Anything is equal to itself – Reflexive; AP is the hypotenuse of both triangles Hyp  Hyp ABP ADPH-L  H-L

  6. Model Problem A D If AB  BC, DC  BC and AC  BD, prove DBCA  DCBD.  E B C DABC and DCBD are right triangles – AB  BC and DC  BC and form right angles, Triangles with right angles are right triangles. AC  BD – We are told so, and both AC & BD are hypotenuses (of DBCA & DCBD respectively) Hyp  Hyp BC  BC – Anything is equal to itself; BC is a leg for both right triangles - Reflexive Leg  Leg DBCA  DCBD because of Hyp - Leg  Hyp - Leg

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