Download 4-3 Reteach Reteach 4-3

Name
4-3
LESSON
Congruent Triangles
Reteach
!
+
*
N!"#N*+,
"
,
Date
Class
Corresponding Parts
Congruent Angles
AB
_ ! JK
_
BC
_ ! KL
_
CA ! LJ
Congruent Sides
_
!A ! !J
!B ! !K
!C ! !L
_
Triangles are congruent if they have the same size and shape. Their corresponding parts,
the angles and sides that are in the same positions, are congruent.
#
9
Z
—
:
4
'
0
1
Y—
Z
.
3
_
PQ
"N
_
YX
6
10
Holt Geometry
To identify corresponding parts of congruent triangles, look at the order of the vertices in the
congruence statement such as "ABC ! "JKL.
8
_
2. YZ !
4. !X !
"Q
"Y
_
6. PN !
X—
_
XZ
&
%
8. y !
2
Given: !XYZ ! !NPQ. Identify the congruent corresponding parts.
1. !Z !
3. !P !
_
5. NQ !
21
62°
22
10. ST !
Given: !EFG ! !RST. Find each value below.
7. x !
9. m!F !
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Name
4-3
LESSON
Reteach
Congruent Triangles continued
_
5. Given
7. Given
%
$
6. Def. of mdpt.
8. Def. of ! "s
.
1
Date
0
#
You can prove triangles congruent by using the definition of congruence.
_
Given: !D and !B are right angles.
!DCE ! !BCA
_ _
C is the midpoint of DB.
_
ED ! AB, EC ! AC
Prove: "EDC ! "ABC
Reasons
1. Given
Proof:
2. Rt. ! ! Thm.
Statements
1. !D and !B are rt. #.
_
4. Third # Thm.
3. Given
_
2. !D ! !B
_
3. !DCE ! !BCA
4. !E ! !A
_
5. C
is the_
midpoint of DB .
_
6. DC ! BC _
_
_
8. "EDC ! "ABC
7. ED ! AB , EC ! AC
Given: !Q ! !R
11. Complete the proof.
_ _
NQ ! SR, NP ! SP
_
P is the midpoint of QR.
Prove: "NPQ ! "SPR
Vert. # Thm.
1. Given
3
2
Class
Reasons
Third # Thm.
Statements
1. !Q ! !R
2. a.
Given
Proof:
2. !NPQ ! !SPR
4. c.
3. b.
Given
5. Def. of mdpt.
_
3. !N ! !S
Def. of ! !s
_
6. e.
_ _
5. d.
7. f.
_
6. NQ ! SR , NP ! SP
QP ! RP
4. P is_
the midpoint
_ of QR .
23
7. "NPQ ! "SPR
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
!
"
Holt Geometry
Name
Date
Class
Practice A
LESSON
4-3
Congruent Triangles
Fill in the blanks to complete each definition.
1.
Corresponding
corresponding
angles and
the same position in polygons with an equal number of sides.
sides are in
congruent
polygons if and only if their
2. Two polygons are
corresponding angles and sides are congruent.
Refer to the figure of !GHI and !JKL for Exercises 3 and 4.
3. Name the three pairs of corresponding sides.
_
_ _
_ _
+
)
_
*
GH ! JK ; HI ! KL ; GI ! JL
4. Name the three pairs of corresponding angles.
'
"G ! "J; "H ! "K; "I ! "L
(
,
Find the value of x.
-
$
X
2
"
39°
&
11
1
4.3
X°
%
,
51°
5. Given: !DEF ! !LMN
!
.
x ! 39
0
#
8.1
6. Given: !ABC ! !PQR
x ! 8.1
7. Etienne flies a kite. When the kite is flying well, the tail sticks out straight
so the indicated angles at V are congruent. Use the phrases from the word
bank to complete this two-column proof.
3
4
Given: "S and "U are right
_angles.
_ _
_
"SVW ! "UVW, SV ! UV , ST ! UT
Prove: !STV ! !UTV
"S ! "U
Third # Thm.
Given
"SVT ! "UVT
5
7
6
Proof:
_
_ _
_
_
Statements
Reasons
_
1. SV ! UV , ST ! UT
1. Given
2. TV ! TV
2. Reflex. Prop. of !
3. "S and "U are right angles.
3. a.
4. b.
"S ! "U
Given
4. Rt. " ! Thm.
5. "SVW ! "UVW
5. Given
6. "SVW and "SVT are supplementary,
"UVW are "UVT are supplementary.
6. Lin. Pair Thm.
7. c.
"SVT ! "UVT
7. ! Suppls. Thm.
Third # Thm.
8. "STV ! "UTV
8. d.
9. !STV ! !UTV
9. Def. of ! !s
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
19
Holt Geometry