4.1 homefun angles of a triangle...4.1 homefun – angles of a triangle examples 1-3: classify each...
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Name_____________________________________________Date____________________Period___________
4.1 Homefun – Angles of a Triangle Examples 1-3: Classify each triangle as acute, equiangular, obtuse or right. 1. ∆𝑈𝑌𝑍 2. ∆𝑈𝑋𝑍 3. ∆𝑈𝑊𝑍 Examples 4-5: Classify each triangle as scalene, isosceles or equilateral. 4. ∆𝐴𝐶𝐷 5. ∆𝐴𝐹𝐷
Example 6: Find 𝒙 and the length of each side if ∆𝑨𝑩𝑪 is an isosceles triangle with 𝑨𝑩̅̅ ̅̅ ≅ 𝑩𝑪̅̅ ̅̅ . 6. Examples 7-8: For each triangle, find 𝒙 and the measure of each side.
7. ∆𝐹𝐺𝐻 is an equilateral triangle with 𝐹𝐺 = 3𝑥 − 10, 𝐺𝐻 = 2𝑥 + 5, and 𝐻𝐹 = 𝑥 + 20
8. ∆𝑅𝑆𝑇 is equilateral. 𝑅𝑆 is three more than four times 𝑥, 𝑆𝑇 is seven more than two times 𝑥, and 𝑇𝑅 is one
more than five times 𝑥. Examples 9-11: Find each measure. 9. 𝑚∠ 4 10. 𝑚∠ 𝐴𝐵𝐶 11. 𝑚∠ 𝐽𝐾𝐿
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Examples 12-17: Find each measure.
12. 𝑚∠ 1 13. 𝑚∠ 2
14. 𝑚∠ 3 15. 𝑚∠ 4
16. 𝑚∠ 5 17. 𝑚∠ 6 Examples 18-25: Find each measure.
18. 𝑚∠ 1 19. 𝑚∠ 2
20. 𝑚∠ 3 21. 𝑚∠ 4
22. 𝑚∠ 5 23. 𝑚∠ 6
24. 𝑚∠ 7 25. 𝑚∠ 8 26. Classify the triangle shown by its angles.
27. The measure of the larger acute angle in a right triangle is two degrees less than three times the measure of the smaller acute angle. Find the measure of each angle. 28. Find the values of y and z in the figure at the right.
(hint: find the value of the linear pair to help solve for 𝑦 to avoid substitution/elimination method)
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Proving Triangles Congruent By SSS, SAS, AAS, ASA– Day 1
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Proving Triangles Congruent – Day 2 – Proofs
1.
2.
3.
Given: Z M
YZ NM
Prove: ΔYXZ ΔNXM
Given: AD CD
AB CB
Prove: ΔABD ΔCBD
Given: 1 4
2 3
Prove: ΔGED ΔEGF
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4.
5.
6.
Given: FG JK
FG JK
Prove: ΔFGH ΔJKH
Given: PR QR
X is the midpoint of PQ
Prove: ΔPXR ΔQXR
Given: RE EP
TP PE
X is the midpoint of EP
Prove: ΔREX ΔTPX
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Proving Triangles Congruent – Day 3 – Congruency Statements
Directions: Decide which two triangles are congruent. If they are explain why, if not, explain why and say, “Not Enough Information.” Simply putting SSS, SAS, ASA, AAS or
NEI is not acceptable.
1. 2. 3.
__________________ __________________ __________________
__________________ __________________ __________________
__________________ __________________ __________________ 4. 5. 6.
__________________ __________________ __________________
__________________ __________________ __________________
__________________ __________________ __________________ 7. 8. 9.
__________________ __________________ __________________
__________________ __________________ __________________
__________________ __________________ __________________
10. 11. 12.
__________________ __________________ __________________
__________________ __________________ __________________
__________________ __________________ __________________ State the 3rd congruence that must be given to prove that RST XYZ , using the indicated
method. (what other corresponding parts are needed) if possible.
CD EB||
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13. Given: RS XY , S T , Prove by ASA 14. Given: YZ ST , T Z , Prove by AAS
16. In the figure ∠𝐻 ≅ ∠𝐿 and 𝐻𝐽 = 𝐽𝐿. Which of the following statements is about congruence is true?
17. Which of the following sets of triangles can be proved congruent
using the AAS Theorem?
18. What information would help prove ABC DEC by ASA? Click all that apply.
Continues on the next page…..
A. ∆𝐻𝐼𝐽 ≅ ∆𝐿𝐾𝐽 by ASA
B. ∆𝐻𝐼𝐽 ≅ ∆𝐾𝐿𝐽 by SSS
C. ∆𝐻𝐼𝐽 ≅ ∆𝐾𝐿𝐽 by SAS
D. ∆𝐻𝐼𝐽 ≅ ∆𝐿𝐾𝐽 by SAS
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19. Given: W Y , WZ YZ , bisects ZX WZY
Prove: XWZ XYZ
Statements Reasons
20. Given: GJ KL , / /KL GJ , K is the midpoint 𝐻𝐺̅̅ ̅̅
Prove: KLH GJK
Statements Reasons
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Formal – Unit 4 – Triangle Congruence – CPCTC
State how the given triangles are congruent, (if possible) then find the requested information.
1. Find BC. 2. Find y. 3. Find AC
Reason: __________________ Reason: __________________ Reason: __________________
𝑩𝑪 =___________________ 𝒚 =___________________ 𝑨𝑪 =___________________
4. Find m ADC 5. Find NQ 6. Find z
Reason: __________________ Reason: __________________ Reason: __________________
𝒎∠𝑨𝑫𝑪 =___________________ 𝑵𝑶 =___________________ 𝒛 =___________________
A D
B C
10
30
3 1y
10x
C
A
72°
56° 52°
56°52°
72°
M N
OP
164x+4 13 z
28
4y
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7. Find AE, given 𝐴𝐸 = 12𝑥 + 13 8. Find x 9. Find SU
𝐸𝐷 = 13𝑥
Reason: __________________ Reason: __________________ Reason: __________________
𝑨𝑬 =___________________ 𝒙 =___________________ 𝑺𝑼 =___________________ Write a congruency statement proving the following statements.
10. Given: H is the midpoint of 𝐸𝑀 ̅̅ ̅̅ ̅& 𝑍𝐾̅̅ ̅̅ 11. Given: Diagram
Prove: EZ KM Prove: W Y
________________________________________ ________________________________________
________________________________________ ________________________________________
________________________________________ ________________________________________ 12.
________________________________________
________________________________________
________________________________________
Continues on the next page…
A
B C
D
E
45°
45°
15
b+9
R
ST
U
V
:
||
||
Given
FJ GK
JG KH
Prove:
J K
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13. Given: 𝐴𝐵̅̅ ̅̅ ||𝐷𝐶̅̅ ̅̅ , 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅
Prove: ∠𝐶𝐷𝐴 ≅ ∠𝐷𝐴𝐶
Statements Reasons
13. Given: 𝐴𝐵̅̅ ̅̅ ||𝐷𝐶̅̅ ̅̅ , 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅
Prove: 𝐵𝐸̅̅ ̅̅ ≅ 𝐸𝐶̅̅ ̅̅
Statements Reasons
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Unit 4 – Formal – Triangle Congruence – HL Worksheet
Directions: Decide which two triangles are congruent. If they are explain why, if not, explain why and say, “Not Enough Information.” Simply putting SSS, SAS, ASA, AAS HL,
or NEI is not acceptable.
1. 2. 3.
__________________ __________________ __________________
_________________ __________________ __________________
__________________ __________________ __________________ 4. 5. 6.
__________________ __________________ __________________
__________________ __________________ __________________
__________________ __________________ __________________
7. 8. 9.
__________________ __________________ __________________
__________________ __________________ __________________
__________________ __________________ __________________ 10. 11. 12.
__________________ __________________ __________________
__________________ __________________ __________________
__________________ __________________ __________________
L RS
A N
W
XY
ZA B
CD
D
F
EG
H
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13. 14. 15.
__________________ __________________ __________________
__________________ __________________ __________________
__________________ __________________ __________________
16. If ∆𝐶𝐸𝐷 ≅ ∆𝑄𝑅𝑃 by HL-congruence, which of the following is true?
A. ∠𝐶 ≅ ∠𝑄, ∠𝐸 ≅ ∠𝑅, ∠𝐷 ≅ ∠𝑃
B. ∠𝐶 ≅ ∠𝑄, ∠𝐸 ≅ ∠𝑃, ∠𝐷 ≅ ∠𝑅
C. ∠𝐶 ≅ ∠𝑃, ∠𝐸 ≅ ∠𝑅, ∠𝐷 ≅ ∠𝑄
D. ∠𝐶 ≅ ∠𝑅, ∠𝐸 ≅ ∠𝑄, ∠𝐷 ≅ ∠𝑃
17. In the figure below, 𝐷𝐸 = 𝐸𝐻, 𝐺𝐻̅̅ ̅̅ ≅ 𝐷𝐹̅̅ ̅̅ , and ∠𝐹 ≅ ∠𝐺. Is there enough information to
conclude that ∆𝐷𝐸𝐹 ≅ ∆𝐻𝐸𝐺? If so, state the congruence postulate that supports the
congruence statement.
A. Yes, by SSA Postulate
B. Yes, by SAS Postulate
C. Yes, by AAS Theorem
D. No, not enough information
18. In the figure 𝐿𝑀̅̅ ̅̅ ≅ 𝑀𝑆̅̅ ̅̅ and 𝑅𝑆̅̅̅̅ ≅ 𝐿𝑂̅̅̅̅ . Which theorem can be used to conclude that
∆𝐿𝑀𝑂 ≅ ∆𝑆𝑀𝑅?
A. SSA
B. AAA
C. SAS
D. HL
Continues on the next page…..
,
int
SP PR TR PR
Q is the Midpo of PR
SQ QT
sec
AC BX
BX bi ts AC at B
A
D
C
B
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19.
Keep Going….
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20. Given: 𝐻𝐺̅̅ ̅̅ ≅ 𝐽𝐻̅̅̅̅ , 𝐺𝐽̅̅ ̅ ⊥ 𝐾𝐻̅̅ ̅̅ . 𝐾𝐻̅̅ ̅̅ bisects 𝐺𝐽̅̅ ̅
Prove: ∆𝐿𝐻𝐺 ≅ ∆𝐿𝐻𝐽
Statements Reasons
21. Given: 𝑅𝐸̅̅ ̅̅ ⊥ 𝐸𝑃̅̅ ̅̅ , 𝑇𝑃̅̅̅̅ ⊥ 𝑃𝐸̅̅ ̅̅ . 𝑋 is the midpoint of 𝐸𝑃̅̅ ̅̅
Prove: ∆𝑅𝐸𝑋 ≅ ∆𝑇𝑃𝑋
Statements Reasons
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Triangle Congruence Review Name: __________________
Directions: Decide which two triangles are congruent. If they are explain why, if not, explain why and say, “Not Enough Information.”
1. 2. 3.
____________________________ ____________________________ ____________________________
____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________
4. 5. 6.
____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________
____________________________ ____________________________ ____________________________
7. 8. 9.
____________________________ ____________________________ ____________________________
____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________
10. 11. 12.
____________________________ ____________________________ ____________________________
____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________
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13. 14. 15.
____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________
State the 3rd congruence that must be given to prove that RST XYZ , using the
indicated method. (what other corresponding parts are needed) if possible.
16. Given: RS XY , TR ZX , Prove by SAS 17. Given: YZ ST , ZX TR , Prove by SSS
18. Given: R X , RS XY , Prove by AAS 19. Given: S Y , Z T , Prove by ASA
20. Given: RS XY , R X , 90 m R , Prove by HL
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21) In the figure below, 𝐷𝐸 = 𝐸𝐻, 𝐺𝐻̅̅ ̅̅ ≅ 𝐷𝐹̅̅ ̅̅ , and ∠𝐹 ≅ ∠𝐺. Is there enough
information to conclude ∆𝐷𝐸𝐹 ≅ ∆𝐻𝐸𝐺? If so, state the congruence postulate that supports the congruence statement.
A. Yes, by SSA Postulate
B. Yes, by SAS Postulate
C. Yes, by AAS Theorem
D. No, not enough information
22) If ∆𝐴𝐵𝐶 ≅ ∆𝑄𝑅𝑃, which of the following is true?
A. ∠𝐴 ≅ ∠𝑄, ∠𝐵 ≅ ∠𝑅, ∠𝐶 ≅ ∠𝑃
B. ∠𝐴 ≅ ∠𝑄, ∠𝐵 ≅ ∠𝑃, ∠𝐶 ≅ ∠𝑅
C. ∠𝐴 ≅ ∠𝑃, ∠𝐵 ≅ ∠𝑅, ∠𝐶 ≅ ∠𝑄
D. ∠𝐴 ≅ ∠𝑅, ∠𝐵 ≅ ∠𝑄, ∠𝐶 ≅ ∠𝑃
23) In the figure ∠𝐺𝐴𝐸 ≅ ∠𝐿𝑂𝐷 and 𝐴𝐸̅̅ ̅̅ ≅ 𝐷𝑂̅̅ ̅̅ . What information is needed to prove
that ∆𝐴𝐺𝐸 ≅ ∆𝑂𝐿𝐷 by AAS?
A. 𝐺𝐸̅̅ ̅̅ ≅ 𝐿𝐷̅̅ ̅̅
B. 𝐴𝐺̅̅ ̅̅ ≅ 𝑂𝐿̅̅̅̅
C. ∠𝐴𝐺𝐸 ≅ ∠𝑂𝐿𝐷
D. ∠𝐴𝐸𝐺 ≅ ∠𝑂𝐷𝐿
24) In the figure ∠𝐻 ≅ ∠𝐿 and 𝐽𝐼 = 𝐽𝐾. Which of the following statements is about
congruence is true?
A. ∆𝐻𝐼𝐽 ≅ ∆𝐿𝐾𝐽 by ASA
B. ∆𝐻𝐼𝐽 ≅ ∆𝐾𝐿𝐽 by SSA
C. ∆𝐻𝐼𝐽 ≅ ∆𝐾𝐿𝐽 by SAS
D. ∆𝐻𝐼𝐽 ≅ ∆𝐿𝐾𝐽 by AAS
25)
Refer To the figure to complete the congruence statement, ∆𝐴𝐵𝐶 ≅ _________. A. ∆𝐴𝐶𝐸
B. ∆𝐸𝐷𝐶
C. ∆𝐸𝐴𝐷
D. ∆𝐸𝐷𝐴
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28. This is a three part questions. Use the diagram below to answer
Part I
What information is needed to prove ∆𝐷𝐴𝐵 ≅ ∆𝐷𝐶𝐵 𝑏𝑦 𝐴𝐴𝑆? Choose all that apply.
a) ∠𝐷𝐴𝐵 ≅ ∠𝐷𝐶𝐵
b) 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅
c) 𝐴𝐵̅̅ ̅̅ ||𝐷𝐶̅̅ ̅̅
d) 𝐴𝐷̅̅ ̅̅ ≅ 𝐵𝐶̅̅ ̅̅
Part II
What information is needed to prove ∆𝐷𝐴𝐵 ≅ ∆𝐷𝐶𝐵 𝑏𝑦 𝑆𝐴𝑆? Choose all that apply.
a) 𝐷𝐵̅̅ ̅̅ ≅ 𝐷𝐵̅̅ ̅̅
b) 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅
c) 𝐴𝐵̅̅ ̅̅ ||𝐷𝐶̅̅ ̅̅
d) 𝐴𝐷̅̅ ̅̅ ≅ 𝐵𝐶̅̅ ̅̅
Part III
What information is needed to prove ∆𝐷𝐴𝐵 ≅ ∆𝐷𝐶𝐵 𝑏𝑦 𝑆𝑆𝑆? Choose all that apply.
a) 𝐷𝐵̅̅ ̅̅ ≅ 𝐷𝐵̅̅ ̅̅
b) 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅
c) 𝐴𝐵̅̅ ̅̅ ||𝐷𝐶̅̅ ̅̅
d) 𝐴𝐷̅̅ ̅̅ ≅ 𝐵𝐶̅̅ ̅̅
26) 27)
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Formal – Unit 4 – Isosceles and Equilateral Triangles
Solve the following.
1) 2) 3)
𝒙 = ______________ 𝒚 = _____________ 𝑨𝑪 = ______________ 𝒙 = _____________ 𝒛 = ______________ 4) 5)
𝒙 = ______________ 𝒛 = ______________ 𝒙 = ______________
6) 7)
𝒏 = ______________ 𝒎 = ______________ 𝒙 = ______________
8) 9)
𝒙 = ______________ 𝒚 = ______________ 𝒛 = ______________ 𝒂 = ______________ 𝒃 = ______________
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10) 11)
𝒈 = ______________ 𝒉 = ______________ 𝒗 = ___________ 𝒘 = ____________
𝒙 = ___________ 𝒚 = ____________
12. Which conclusion can be drawn from the given facts in the diagram?
A. 𝑇𝑄̅̅ ̅̅ bisects ∠𝑃𝑇𝑆
B. ∠𝑇𝑄𝑆 ≅ ∠𝑅𝑄𝑆
C. 𝑃𝑇̅̅̅̅ ≅ 𝑅𝑆̅̅̅̅
D. 𝑇𝑆 = 𝑃𝑄
13. In the figure, 𝐴𝐶̅̅ ̅̅ ≅ 𝐴𝐵̅̅ ̅̅ . Find the value of x in terms of y.
A. 𝑥 = −2𝑦 + 160
B. 𝑥 = 4𝑦 − 140
C. 𝑥 = −4𝑦 + 40
D. 𝑥 = 𝑦 + 10
14.
:
.
.
,
, 27
24
2 7
3 23
4 105
Given
H is the midpt of GJ
M is the midpt of OK
GO JK GJ OK
G K OK
m GOH x
m GHO y
m JMK y
m MJK x
_______
_______
________
Find
m GOH
m GHO
GH
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Unit 4 – Formal – Unit Review Name: _____________________
1) If ∆𝐶𝐸𝐷 ≅ ∆𝑄𝑅𝑃, which of the following is true?
A. ∠𝐶 ≅ ∠𝑄, ∠𝐸 ≅ ∠𝑅, ∠𝐷 ≅ ∠𝑃
B. ∠𝐶 ≅ ∠𝑄, ∠𝐸 ≅ ∠𝑃, ∠𝐷 ≅ ∠𝑅
C. ∠𝐶 ≅ ∠𝑃, ∠𝐸 ≅ ∠𝑅, ∠𝐷 ≅ ∠𝑄
D. ∠𝐶 ≅ ∠𝑅, ∠𝐸 ≅ ∠𝑄, ∠𝐷 ≅ ∠𝑃
2) In the figure ∠𝐺𝐴𝐸 ≅ ∠𝐿𝑂𝐷 and 𝐴𝐸̅̅ ̅̅ ≅ 𝐷𝑂̅̅ ̅̅ . What information is needed to prove that ∆𝐴𝐺𝐸 ≅ ∆𝑂𝐿𝐷 by SAS?
A. 𝐺𝐸̅̅ ̅̅ ≅ 𝐿𝐷̅̅ ̅̅
B. 𝐴𝐺̅̅ ̅̅ ≅ 𝑂𝐿̅̅̅̅
C. ∠𝐴𝐺𝐸 ≅ ∠𝑂𝐿𝐷
D. ∠𝐴𝐸𝐺 ≅ ∠𝑂𝐷𝐿
3) In the figure ∠𝐻 ≅ ∠𝐿 and 𝐻𝐽 = 𝐽𝐿. Which of the following statements is about congruence is true?
A. ∆𝐻𝐼𝐽 ≅ ∆𝐿𝐾𝐽 by ASA
B. ∆𝐻𝐼𝐽 ≅ ∆𝐾𝐿𝐽 by SSS
C. ∆𝐻𝐼𝐽 ≅ ∆𝐾𝐿𝐽 by SAS
D. ∆𝐻𝐼𝐽 ≅ ∆𝐿𝐾𝐽 by SAS
4) Refer To the figure to complete the congruence statement, ∆𝐴𝐵𝐶 ≅ _________.
A. ∆𝐴𝐶𝐸
B. ∆𝐸𝐷𝐶
C. ∆𝐸𝐴𝐷
D. ∆𝐸𝐷𝐴
5) Which theorem can be used to conclude that ∆𝐶𝐴𝐵 ≅ ∆𝐶𝐸𝐷?
A. SAA
B. SAS
C. SSS
D. AAA
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6) Which of the following sets of triangles can be proved congruent using the AAS Theorem?
A.
C.
B.
D.
7) You are given the following information about ∆𝐺𝐻𝐼 and ∆𝐸𝐹𝐷.
I. ∠𝐺 ≅ ∠𝐸
II. ∠𝐻 ≅ ∠𝐹
III. ∠𝐼 ≅ ∠𝐷
IV. 𝐺𝐻̅̅ ̅̅ ≅ 𝐸𝐹̅̅ ̅̅ V. 𝐺𝐼̅̅ ̅ ≅ 𝐸𝐷̅̅ ̅̅
Which combination cannot be used to prove that ∆𝐺𝐻𝐼 ≅ ∆𝐸𝐹𝐷?
A. V, IV, II
B. II, III, V
C. III, V, I
D. All of the above prove ∆𝐺𝐻𝐼 ≅ ∆𝐸𝐹𝐷
8) In the figure 𝐿𝑀̅̅ ̅̅ ≅ 𝑀𝑆̅̅ ̅̅ and 𝑅𝑆̅̅̅̅ ≅ 𝐿𝑂̅̅̅̅ . Which theorem can be used to conclude that ∆𝐿𝑀𝑂 ≅ ∆𝑆𝑀𝑅?
A. SSA
B. AAA
C. SAS
D. HL
11) In the figure, ∆𝐴𝐵𝐶 ≅ ∆𝐴𝐹𝐷. What is the 𝑚∠𝐷?
A. 𝑚∠𝐷 = 57°
B. 𝑚∠𝐷 = 42°
C. 𝑚∠𝐷 = 30°
D. 𝑚∠𝐷 = 25°
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13) In the figure, 𝐴𝐶̅̅ ̅̅ ≅ 𝐴𝐵̅̅ ̅̅ . Find the value of y in terms of x.
A. 𝑦 = −3𝑥 + 160
B. 𝑦 = 6𝑥 − 140
C. 𝑦 = 6𝑥 + 40
D. 𝑦 =3𝑥 + 20
2
14) Given: AEB CDB . Why is AEB DCB ?
a) SSS b) SAS c) ASA d) AAS
e) HL f) CPCTC g) Not Possible
State all the ways (if possible) the given two triangles are congruent.
15. 16. 17. 18.
19. 20. 21. 22.
12) Given ∆𝑀𝑁𝑃, Anna is proving 𝑚∠1 + 𝑚∠2 = 𝑚∠4. Which statement should be part of her proof?
A. 𝑚∠1 = 𝑚∠2
B. 𝑚∠1 = 𝑚∠3
C. 𝑚∠1 + 𝑚∠3 = 180°
D. 𝑚∠3 + 𝑚∠4 = 180°
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23. 24. 25. 26.
State the 3rd congruence that must be given to prove that RST XYZ , using the indicated method.
(what other corresponding parts are needed) if possible.
27. Given: RS XY , TR ZX , Prove by SAS 28. Given: YZ ST , ZX TR , Prove by SSS
29. Given: R X , RS XY , Prove by AAS 30. Given: S Y , Z T , Prove by ASA
31. Given: RS XY , R X , 90 m R , Prove by HL
Label the following triangles by their sides and angles. Then find the following.
32. 33.
Triangle Name: _____________________ Triangle Name: _____________________
𝒆 =_______________ 𝒃 =_______________ 𝒘 =_______________ 𝑳 =_______________
369w
6L
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34. Given:
∆𝑭𝑬𝑫 is equilateral
𝑮𝑬̅̅ ̅̅ ⊥ 𝑫𝑬̅̅ ̅̅ 𝒎∠𝑭𝑬𝑮 = 𝒙 + 𝒚
𝒎∠𝑫 = 𝟑𝒙 − 𝟔 𝒎∠𝑭 = 𝟔𝒚 + 𝟏𝟐
Find: 𝒙, 𝒚, and 𝒛
35. Given:
𝒎∠𝑨 = 𝒙𝟐 𝒎∠𝑩 = 𝟏𝟏𝒙
𝒎∠𝑩𝑪𝑫 = 𝟏𝟎𝟐°
Find: x
36. Given:
∆𝑨𝑩𝑪 is isosceles with base 𝑩𝑪̅̅ ̅̅
𝒎∠𝑨 = 𝟔𝒚 𝒎∠𝑩 = 𝟖𝒚 + 𝟒𝒙
𝑨𝑪 = 𝒙 + 𝒚
Find: 𝑨𝑩
37. Given:
∆𝑨𝑩𝑪 is isosceles ∆𝑨𝑬𝑪 is isosceles ∆𝑨𝑫𝑪 is equilateral 𝒎∠𝟗 = 𝒎∠𝟏 = 𝒎∠𝟑
Find: angles 1 – 9
𝑚∠1 =
𝑚∠2 =
𝑚∠3 =
𝑚∠4 =
𝑚∠5 =
𝑚∠6 =
𝑚∠7 =
𝑚∠8 =
𝑚∠9 =
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38. Given: 𝐴𝐵̅̅ ̅̅ ||𝐷𝐶̅̅ ̅̅ , 𝐴𝐷̅̅ ̅̅ ⊥ 𝐷𝐶̅̅ ̅̅ , 𝐵𝐶̅̅ ̅̅ ⊥ 𝐷𝐶̅̅ ̅̅ ,
Prove: 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅
Statements Reasons
39. Given: 𝐻 is the midpoint of 𝐸𝑌̅̅̅̅̅ and 𝑍𝑇̅̅̅̅
Prove: ∆𝐸𝐻𝑍 ≅ ∆𝑌𝐻𝑇
Statements Reasons