Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Do Now: Aim: How to prove triangles are congruent using a 5 th shortcut: Hyp-Leg. 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 x a 2 + b 2 = c 2 Pythagorean Theorem x = 20 2 a c b x = 400 x 2 = 144 x = 12 12

Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Hypotenuse-Leg V. HYP-LEG If hypotenuse AC  hypotenuse A’C’, and leg BC  leg B’C’ then right  ABC  right  A’B’C’ If the Hyp-Leg  Hyp-Leg, then the right triangles are congruent  ABC and  A’B’C’ are right triangles A CBB’C’ A’

Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Model Problem  ABC, BD  AC, AB  CB. Explain why  ADB   CDB.  ABC and  CBD 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  ABD &  BDC respectively) Hyp  Hyp BD  BD – Anything is equal to itself; BD is a leg for both right triangles - Reflexive Leg  Leg  ADB   CDB because of Hyp - Leg  Hyp - Leg

Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Model Problem  ABD is right,  CDB is right, AD  CB. Explain why  ADB   CDB.  ABD and  CBD are right triangles – Triangles with right angles are right triangles. AD  CB – We are told so, and both AC & BD are hypotenuses (of  BCA &  CBD respectively) Hyp  Hyp BD  BD – Anything is equal to itself; BD is a leg for both right triangles - Reflexive Leg  Leg  ADB   CDB because of Hyp - Leg  Hyp - Leg

Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Model Problem PB  AC, PD  AE, AB  AD. Explain why  ABP   ADP  ADP and  ABP 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   ADP H-L  H-L

Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Model Problem E AD If AB  BC, DC  BC and AC  BD, prove  BCA   CBD.   ABC and  CBD 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  BCA &  CBD respectively) Hyp  Hyp BC  BC – Anything is equal to itself; BC is a leg for both right triangles - Reflexive Leg  Leg  BCA   CBD because of Hyp - Leg  Hyp - Leg B C