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NAME _______________________________________ DATE _______ SCORE _______
Some Ways to Prove Triangles
Congruent
Suppose D.RED
1. LE := L
3. RE
I For use after Section 4-2 I
=D.SUN. Complete.
= mLN
2. -nv t.. D
...:;.
1)______
= _,S=U~-
4. ED:=
5. D. DRE := D PSll
1./A/
6. 6E0ft.
:= D. UNS
The two triangles shown are congruent. Complete.
7. D. BAD :=
8. LN :=
Af/kftl
LO
, because ___,.C:. .P
r. --=C=T
. '-'C
"----------------- - B
9. . IJA
= FA; A
is the midpoint of
A
F
Exs. 7- 9
(jt=
. Can the two triangles be proved congruent? If so, what postulate
can be used?
10.~
11.
12.
13.
14.
15.
~
A
S
Supply the missing reasons in the proof.
-16. Given: CA := DA; .
BA :=EA
Prove: D. BCA := D. EDA
Proof:
Statements ·
1. CA := DA; BA := EA
Reasons
2. LBAC :=LEAD
1. -7
~
~~----------2. ~; L Ls S"
3. D. BCA := D. EDA
3.
PRACTICE MASTERS for GEOMETRY
Copyright © by Houghton Mifflin Company. All right s reserved .
' oi..S
17
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11r cw
~"t..
~ /4-0
-
fhe SSS, SAS, and ASA Postulates give us three methods of proving triangles
congruent. In this section we will develop two other methods.
AAS Theorem
If two angles and a non-included side of one triangle are congruent to the
corresponding parts of another triangle, then the triangles are congruent.
Given: !:::.ABC and !:::.DEF; L B
L C
=L F; AC =DF
Prove: !:::.ABC
= L E;
= !:::.DEF
s
'-f3 :: L e
R.
LC.. ~L ~
AG
~DF
DIV!JC ~ 0 Def
Our final method of proving triangles congruent applies
only to right triangles. In a right triangle the side opposite
the right angle is called the hypotenyse (hyp.). The other two
sides are called legs.
leg
HL Theorem
If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.
Given: !:::.ABC and !:::.DEF;
LC an~LF are right~;
AB = DE (hypotenuses);
BC = EF (legs)
Prove: !:::.ABC = !:::.DEF
A
B
E
c
F
SAS
\
Classroom Exercises -
- - __
State which congruence method(s) can be used to prove the triangles
congru~
If no method applies, say none.
2.
1.
3.
1.1: 2. w
~
..ix,-A (AAs)
~ HL
~
p.p.s:. en- (SA~)
(ASA~
,
.,. , )f
--7.~
.
A
7.~
none
..
8. .
8.
~
9.
ASA
SAS
~·
HL
AAS
. none
AA> .P 1\5 A
ti/11./IJi' II~
L-
c. W 'p,.,.A 1
For each diagram, name a pair of overlapping triangles. Tell whether the
triangles are congruent by the SSS, SAS, ASA, AAS, or HL method.
-
--
10. Given: AB =: DC;
11. Given: L 2
L 3;
p
L
~
C
==
L 1 =: L4
AC =: DB
M
D
N
p
AI
M
6.MP'Jl =b. fJ LM.
12. Given: WU =: ZV·
'
13. Given: L ABC =: L ACB ;
AE .l EC;·
WX = ·YZ;
L U and L V are rt. ~ .
-
-
AD .l DB
A
W
z
y
X
u
A
v
~
y
W X
!J. UWY = !J. vzx by HL
z
!J. ADB
!J. EBC
B~C
= !J. AEC by AAS
=!J. DCB
by AAS
> kSA