REVIEW OF THE PROBLEMS THAT ARE ON THE CHAPTER 4 EXAM

Chapter 4 Exam

1. If BCDE is congruent to OPQR, then is congruent to __?__.

A. B. C. D.

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A. B. C. D.

1. If BCDE is congruent to OPQR, then is congruent to __?__.

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1. because B is the first letter and corresponds to O and E is the last letter corresponding to R.

B

C

E

D

O

P Q

R

2. Given ΔABC ≌ ΔPQR, m∠B = 4v+1, and m∠Q = 8v-7, find m∠B and m∠Q.

A. B. C. D.

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A. 26B. 10C. 9D. 23

2. Given ΔABC ≌ ΔPQR, m∠B = 4v+1, and m∠Q = 8v-7, find m∠B and m∠Q.

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Since ∠B corresponds to ∠Q

Plugging in 2

3. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to

scale.

A. B. C. D.

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d°

e°f°

b

c

g

3

45

57°

33°

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A. 5B. 57C. 4D. 3

3. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to

scale.

d°

e°f°

b

c

g

3

45

57°

33°

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A. 3 is the bottom side length and c is in the corresponding part so

4. Justify the last two steps of the proof.

A. B. C. D.

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A. Symmetric Prop of ≌; SSSB. Reflexive Prop of ≌; SSSC. Symmetric Prop of ≌; SASD. Reflexive Prop of ≌; SAS

4. Justify the last two steps of the proof.

4-2A. Reflexive Prop of ≌B. SSS

5. Name the angle included by the sides and .

A. B. C. D.

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N

P

M

A. ∠PB. ∠NC. ∠MD. none of these

5. Name the angle included by the sides and .

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N

P

M

∠N because it touches both of the listed sides.(Same letter in both sides is always the included angle.)

A

B C D

( (

6. What other information do you need in order to prove the triangles congruent using the SAS Congruence

Postulate?

A. B. C. D.

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A.

6. What other information do you need in order to prove the triangles congruent using the SAS Congruence

Postulate?

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A

B C D

( (We know Reflexive no because that is AAS no because already marked so not additional information.

No because that is ASA

So correct answer is D because side included angle side SAS.

A. B. C. D.

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7. What is the missing reason in the two-column proof?

A. AAS TheoremB. SAS PostulateC. SSS PostulateD. ASA Postulate

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7. What is the missing reason in the two-column proof?

D. ASA Postulate

ASA Postulate

8. Name the theorem or postulate that lets you immediately conclude ΔABD ≌ ΔCBD.

A. B. C. D.

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A

D

C

B

||

A. AASB. ASAC. SASD. None of these

8. Name the theorem or postulate that lets you immediately conclude ΔABD ≌ ΔCBD.

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A

D

C

B

||

Reflexive

So ΔABD ≌ ΔCBD by SAS

9. Based on the given information, what can you conclude, and why?

A. B. C. D.

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A. by SASB. by SASC. by ASAD. by ASA

9. Based on the given information, what can you conclude, and why?

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1. Since because of vertical angles

2. by ASA

10. R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and

tell which segment is congruent to

A. B. C. D.

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A. by SAS; B. by AAS; C. by ASA; D. No, the two triangles are not

congruent.

10. R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and

tell which segment is congruent to

4-4

R

S

T E

F

D60o

100o 60o

20o

44

100o20o

Since triangles add up to 180 degrees .So by ASAAnd

11. Supply the missing reasons to complete the proof.

A. B. C. D.

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A. AAS; Corres. parts of ≌ Δ are ≌B. SAS; Corres. parts of ≌ Δ are ≌C. ASA; D. ASA; Corres. parts of ≌ Δ are ≌

11. Supply the missing reasons to complete the proof.

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1. ASA2. Corres. parts of ≌

Δ are ≌

12. Write a two-column proof.

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13. What is the value of x?

A. B. C. D.

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48°

Drawing not to scale

2121

xº

A. 66o

B. 71o

C. 132o

D. 142o

13. What is the value of x?

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48°

Drawing not to scale

2121

xº

Answer is A 66o

14. The legs of an isosceles triangle have lengths 3x+2 and 2x+6. The base has length 4x + 3. What is the

length of the base?

A. B. C. D.

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A. 4B. 14C. 19D. Cannot be determined

14. The legs of an isosceles triangle have lengths 3x+2 and 2x+6. The base has length 4x + 3. What is the

length of the base?

4-5 Correct answer is C. 19

15. Find the values of x and y.

A. B. C. D.

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A

DB C

((

66°

Drawing not to scale

y°

x°

A. x = 24; y = 66B. x = 66; y = 24C. x = 90; y = 66D. x = 90; y = 24

15. Find the values of x and y.

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A

DB C

((

66°

Drawing not to scale

y°

x°

Since bisects the vertex angle, is the perpendicular bisector of so x = 90

The angles of a triangle add up to 180 degrees

The correct answer is D x = 90; y = 24

16. What additional information will allow you to prove the triangles congruent by the HL

Theorem?

A. B. C. D.

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A

E

B

D

C

|

|

A. A ≌ ∠EB. m∠BCE =90

A

E

B

D

C

|

|

16. What additional information will allow you to prove the triangles congruent by the HL

Theorem?

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A. A ≌ ∠E is not correct AAS B. m∠BCE =90 is outside the triangle so does not help. C. Right Δ, ≌ Hypotenuses,

and ≌ legs so yes HLD. does not work because is

not a side of a triangle.

17. For which situation could you immediately prove Δ1 ≌ Δ2 using the HL Theorem?

A. B. C. D.

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A. I onlyB. II onlyC. III onlyD. II and III

17. For which situation could you immediately prove Δ1 ≌ Δ2 using the HL Theorem?

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I. Would be congruent by ASA does not have hypotenuses ≌ so not HL

II. Would be congruent by SAS again does not have hypotenuses ≌ so not HL

III. Right Triangles, hypotenuses are ≌, and they have a leg in common so definitely HL

Correct answer is C. III only

18. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?

A. B. C. D.

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A

CB D

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A. Yes; ΔCAB≌ΔDAC.B. Yes; ΔACB≌ΔACD.C. Yes; ΔABC≌ΔACD.D. No, the triangles

cannot be proven congruent

18. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?

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A

CB D

| |

1. Given right angles we have right triangles.

2. Since we have congruent hypotenuses.

3.

4.Yes; ΔACB≌ΔACD by HL.

Correct answer is B.

19. What common side do ΔCDE and ΔFED share?

A. B. C. D.

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A

G

E

B

D

H

C

F

19. What common side do ΔCDE and ΔFED share?

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A

G

E

B

D

H

C

F

They have side in common correct answer is A.

20. What common angle do ΔACF and ΔBCG?

A. B. C. D.

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C

G

AB

F

A. ∠BB. ∠AC. ∠CD. ∠F

20. What common angle do ΔACF and ΔBCG?

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C

G

AB

F They have angle ∠C in common correct answer is C.

Chapter 4 Exam TOMORROW!

Journals due Friday

Portfolio Due Friday