Geometry Section 4.6
Notes
Name____________________________
Target Goals:
1. I will be able to prove right triangles congruent using Hypotenuse Leg Theorem.
REVIEW!
Tell which postulate can be used to prove the triangles congruent or write not possible.
Find the measures of each missing variable.
Given: HUE is isosceles (Base HE )
OX SE
Prove: OX  OH
NEW STUFF!
Label the parts of a right triangle:
What are the 4 ways we prove triangles congruent?
1.
3.
2.
4.
Now I have a confession to make….there is one more way to prove triangles congruent!
HOWEVER!!!!! This only happens in RIGHT TRIANGLES ONLY.
With right triangles, we can use a method called: Hypotenuse Leg (HL). In order to use HL we
need the following:



Right Triangles
Congruent Hypotenuses.
Pair of congruent legs.
Directions: Use the theorems to find the values of x and y so that CAT  DOG. Show work.
1.
Use SAS
2.
Use HL
C
D
T
56
G
O
2x + 4
D
2x + 3
2y - 9
23
A
C
A
T
3y + 10
4x - 1
O
G
4y - 20
3. Given: XYZ is isosceles
XM  YZ
X
Prove: XMY  XMZ
Y
4.
C
Given: CA  DA
BC  AC
BD  AD
Prove: BC  BD
M
B
1
A 2
D
Z
5.
Given: M is midpoint of NL .
NO  MP
Prove: OM  PL
6. Given: IH is the  bisector of GJ.