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

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)

Proving Triangles Congruent By SSS, SAS, AAS, ASA– Day 1

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

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

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||

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

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

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

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

13. Given: 𝐴𝐵̅̅ ̅̅ ||𝐷𝐶̅̅ ̅̅ , 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅

Prove: ∠𝐶𝐷𝐴 ≅ ∠𝐷𝐴𝐶

Statements Reasons

13. Given: 𝐴𝐵̅̅ ̅̅ ||𝐷𝐶̅̅ ̅̅ , 𝐴𝐵̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅

Prove: 𝐵𝐸̅̅ ̅̅ ≅ 𝐸𝐶̅̅ ̅̅

Statements Reasons

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

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

19.

Keep Going….

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

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.

____________________________ ____________________________ ____________________________

____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________

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

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

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)

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 = ______________

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

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

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°

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°

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

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 =

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