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Name Class Date
4-1 Practice Form G
Congruent Figures
Each pair of polygons is congruent. Find the measures of the numbered angles.
1. 2. S T 3. A F
GH AB MN
1 110 3 5 7
L I F C R 135 P W 4 U
2 120 50 140 B G 8
6
K J ED Q V D E
YX
ml15110; ml25120 ml3590; ml45135 ml55140; ml6590;
ml7540; ml8590
kCATOkJSD. List each of the following. A S
4. three pairs of congruent sides D
CAOJS, ATOSD, CTOJD
5. three pairs of congruent angles
lCOlJ, lAOlS, lTOlD T
C J
WXYZOJKLM. List each of the following.
W J
6. four pairs of congruent sides X M
WZOJM, WXOJK, XYOKL, ZYOML Z
7. four pairs of congruent angles
lWOlJ, lXOlK, lYOlL, lZOlM Y L K
For Exercises 8 and 9, can you conclude that the triangles are congruent?
Justify your answers.
8. nGHJ and nIHJ Yes; lGHJ OlIHJ 9. nQRS and nTVS No; lQSR OlTSV
by Third Angles Thm. because vert.
G and by the Refl . Prop. R angles are
JH O JH. Therefore, congruent, and
kGHJOkIHJ by the lQRSOlTVS
J H Def. of O triangles. 95 S T by Third Angles
Q 95 Thm., but none
of the sides
I are necessarily
V congruent.
10. Developing Proof Use the information given in the diagram. LM
Give a reason that each statement is true.
a. /L>/Q Given N
b. /LNM>/QNP Vert. angles are O.
c. /M>/P Third Angles Thm.
d. LM>QP, LN>QN, MN>PN Given PQ
e. nLNM>nQNP Def. ofOtriangles
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
3
Name Class Date
4-1 Practice (continued) Form G
Congruent Figures
For Exercises 11 and 12, can you conclude that the fi gures are congruent?
Justify your answers.
11. AEFD and EBCF No; answers may 12. nFGH and nJKH Yes; answers may
vary. Sample: vary. Sample:
E B lD does not have to F K
A lFOlJ and
be a right angle. H lGOK by the
Alt. Int. Angles
Thm. and
DFC G J lFHGOlJHK by
the Vert. Angles
Thm., so all
Algebra Find the values of the variables. corresp. parts are
5 congruent.
13. 13 14. 2x 10
74 (5x)
(3x 2)
Algebra ABCD O FGHJ. Find the measures of the given angles or lengths of
the given sides.
15. m/B 5 3y, m/G 5 y 1 50 75 16. CD 5 2x 1 3; HJ 5 3x 1 2 5
17. m/C 5 5z 1 20, m/H 5 6z 1 10 70 18. AD 5 5b 1 4; FJ 5 3b 1 8 14
19. LMNP > QRST. M Q R
Find the value of x. 35 L 45 (3x)
(5x) T
P x
N
S
20. Given: BD is the angle bisector of /ABC. B
BD is the perpendicular bisector of AC.
Prove: nADB > nCDB
Because BD is the angle bisector of lABC, lABD OlCBD. A D C
Because BD is the perpendicular bisector of AC, AD O CD
and lADBOlCDB. BDOBD by the Refl exive Property of
Congruence. So, because the corresponding parts are all
congruent, kABD OkCBD.
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
4
Name Class Date
4-2 Practice Form G
Triangle Congruence by SSS and SAS
Draw kMGT. Use the triangle to answer the questions below. G
1. What angle is included between GM and MT? lM
2. Which sides include /T? GT and TM
M T
3. What angle is included between GT and MG? lG
Would you use SSS or SAS to prove the triangles congruent? If there is not
enough information to prove the triangles congruent by SSS or SAS, write not
enough information. Explain your answer.
4. R 5. E 6. K
H L
P F R M O
D F SAS; two pairs of SSS; three pairs of
N J corresponding sides and corresponding sides
Not enough information; their included angle are are congruent.
two pairs of corresponding congruent.
sides are congruent, but
the congruent angle is not
included.
7. Z 8. P L C 9. A E F
X
W Y A N K B
C D
Not enough information; SSS; three SAS; two pairs of
two pairs of corresponding corresponding corresponding sides
sides are congruent, but sides are and their included right
the congruent angle is not congruent. angle are congruent.
the included angle.
10. O N 11. S 12. C
P
T
T D H
R E G
Not enough information; F
one pair of corresponding SAS; two pairs of R
sides and corresponding corresponding sides SSS or SAS; three pairs
angles are congruent, and their included of corresponding sides
but the other pair of vertical angles are are congruent, or, two
corresponding sides that congruent. pairs of corresponding
form the included angle sides and their included
must also be congruent. vertical angles are
congruent.
Prentice Hall Gold Geometry · Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
13
Name Class Date
4-2 Practice (continued) Form G
Triangle Congruence by SSS and SAS
13. Draw a Diagram A student draws nABC and nQRS. ! e following sides
and angles are congruent:
AC > QS AB>QR /B>/R
Based on this, can the student use either SSS or SAS to prove that nABC > nQRS?
If the answer is no, explain what additional information the student needs. Use a sketch
to help explain your answer. A Q
No; lB and lR are not the
included angles for the sides
given. To prove congruence, you
would need to know either that
BCORS or lQOlA.
B C R S
14. Given: BC > DC, AC > EC B E
Prove: nABC > nEDC C
Statements Reasons A
D
1) BC O DC 1) Given
2) AC O EC 2) Given
3) lBCA O lDCE 3) Vertical © are O.
4) kABC O kEDC 4) SAS
15. Given: WX 6 YZ, WX > YZ W X
Prove: nWXZ > nYZX
Statements Reasons
1) WX n YZ 1) Given Z Y
2) lWXZOlYZX 2) Alternate Interior © are O.
3) WX O YZ 3) Given
4) ZX O XZ 4) Refl exive Property
5) kWXZO kYZX 5) SAS
16. Error Analysis nFGH and nPQR are both equilateral triangles. Your
friend says this means they are congruent by the SSS Postulate. Is your friend
correct? Explain. Incorrect; both triangles being equilateral means that the three
angles and sides of each triangle are congruent, but there is no information
comparing the side lengths of the two triangles.
17. A student is gluing same-sized toothpicks together to make triangles. She
plans to use these triangles to make a model of a bridge. Will all the triangles
be congruent? Explain your answer. Yes; because all the triangles are made from the
same-sized toothpick, all three corresponding sides will be congruent.
Prentice Hall Gold Geometry · Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
14
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