Download Triangle Congruence: ASA, AAS, and HL

Name
Date
LESSON
4-5
Class
Reteach
Triangle Congruence: ASA, AAS, and HL
Angle-Side-Angle (ASA) Congruence Postulate
If two angles and the included side of one triangle are congruent to two angles and the
included side of another triangle, then the triangles are congruent.
_
!
AC is the included
side of /A and /C.
#
_
$
"
DF is the included
side of /D and /F.
%
&
N!"# N$%&
Determine whether you can use ASA to prove the triangles
congruent. Explain.
%
M
,
CM
.
0
'
8
&
CM
+
1
-
1. nKLM and nNPQ
_
:
9
M
2. nEFG and nXYZ
_
Yes; /K > /N, KL > NP, and
No; you need to know that
/L > /P as given.
GF > ZY.
0
_
_
+
3
6
.
-
7
,
4
5
3. nKLM and nPNM,
given that M is the
_
midpoint of NL
4. nSTW and nUTV
_
_
No; you need to know that
Yes; /W > /V and TW > TV as
/NMP > /LMK.
given. /STW > /UTV by the
Vert. ? Thm.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
38
Holt Geometry
Name
LESSON
4-5
Date
Class
Reteach
Triangle Congruence: ASA, AAS, and HL continued
Angle-Angle-Side (AAS) Congruence Theorem
If two angles and a nonincluded side of one triangle are congruent to the corresponding
angles and nonincluded side of another triangle, then the triangles are congruent.
_
_
*
FH is a nonincluded
side of /F and /G.
(
'
+
JL is a nonincluded
side of /J and /K.
,
N&'( N*+,
Special theorems can be used to prove right triangles congruent.
Hypotenuse-Leg (HL) Congruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of
another right triangle, then the triangles are congruent.
*
+
-
.
0
,
N*+,N-.0
5. Describe the corresponding parts and the justifications
for using them to prove the triangles congruent by AAS.
!
"
_
Given: BD is the angle bisector of /ADC.
$
Prove: nABD > nCBD
#
/A > /C (Given), /ADB > /CDB (Def. of / bisector),
_
_
BD > BD (Reflex. Prop. of >)
Determine whether you can use the HL Congruence Theorem to
prove the triangles congruent. If yes, explain. If not, tell what else
you need to know.
6
4
5
0
7
3
2
8
6. nUVW > nWXU
7. nTSR > nPQR
_ _
Yes; UV > WX (Given) and
_ _
No; you need to know that
_
UW > UW (Reflex. Prop. of >)
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
1
_
TR > PR.
39
Holt Geometry