Download Lesson 5.4A: HL Theorem

Lesson 5.4A: HL Theorem
As we have seen, SSS, ASA, SAS, and AAS are postulates/theorems that provide sufficient evidence for
congruence of triangles.
In general, if you know the lengths of two sides of a triangle and the measure of an angle that is not included
between them, two different triangles are possible; thus ASS is not sufficient evidence for triangle congruence.
BUT, there is a special case for the congruence of ____________________________________________.
Quick study of a right triangle:
Hypotenuse-Leg Congruence Theorem (HL):
D
A
C
B
F
E
___________ and ___________ are RIGHT TRIANGLES,
___________
~
= ___________ (HYPOTENUSE)
___________
~= ___________ (LEG)
Therefore, ___________
~
= ___________ by _____________
Are the pairs of triangles below congruent? Justify your decision.
A
D
P
O
1.
2.
3.
Q
R
B
C
U
Y
4.
5.
6.
7.
8.
9.
10.
11.
S
G
13. Use the given in information to sketch ΔLMN and ΔSTU.
Mark the triangles with the given information.
Are the triangles congruent? Justify.
ML
LN, TS
12.
14. What additional piece of information would you
need to know in order to prove the triangles
below are congruent by HL?
T
~
~
SU, LN = SU, MN = TU
R
X
B
Y
Lesson 5.4B: Proofs Using HL
Given:
C
Prove:
C and
D are right angles, CB ~= DB
ΔCAB ~= ΔDAB
Statements
A
Justifications
B
D
Given:
Prove:
A
C is the midpoint of AX
BCY is isosceles with base BY
A and
X are right angles
C
X
~
ΔABC = ΔXYC
Statements
Justifications
B
Y