Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Do Now: Aim: How to prove triangles...
6
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. 16 20 x a 2 + b 2 = c 2 Pythagore an Theorem x 2 + 16 2 = 20 2 a c b x 2 + 256 = 400 x 2 = 144 2 144 x x = 12 12
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Transcript of Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Do Now: Aim: How to prove triangles...
Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry
Do Now:
Aim: How to prove triangles are congruent using a 5th 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.
16
20x
a2 + b2 = c2
Pythagorean Theorem
x2 + 162 = 202
a c
b
x2 + 256 = 400x2 = 144
2 144x 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
CB B’ C’
A’
Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry
Model Problem
DA C
B
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
B C
A D
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
B
PA
C
E
Q
D
Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry
Model Problem
E
A DIf 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
