Middle “Bubble”

HL: “Hypotenuse-Leg”

If the hypotenuse and a leg of one triangle are congruent to the corresponding parts of another right triangles, then the triangles are congruent.

A

B C

F

K

B

“HYPOTENUSE LENGTH”

4.3: HL

Given C is the midpoint of BD, and AB=DE, prove that ABC~ EDC

A

B

C

D

EStatements Reasons

1.) AB=DE 1.) Given

2.) BC=DC

2.) Definition of Midpoint

3.) m<ACB=m<DCE

3.) Vertical Angles

4.) m<ACB=90 4.) Substitution/Transitive

5.) ABC = EDC

5.) HL

Proof of HL: 2 right triangles with same hypotenuse and leg

Given 2 right triangles with sides of length a,b,c and d,b,c

a

bc

d

b cProve a=d

a + b = cPythagorean theorem

d + b= c

“ “

2 2 2

2 2 2

a + b = d + b

22 22 Substitution/transitive

a = d22 Subtraction Property

a=d Square root both sides