review of the problems that are on the chapter 4 exam chapter 4 exam
TRANSCRIPT
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REVIEW OF THE PROBLEMS THAT ARE ON THE CHAPTER 4 EXAM
Chapter 4 Exam
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1. If BCDE is congruent to OPQR, then is congruent to __?__.
A. B. C. D.
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A. B. C. D.
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1. If BCDE is congruent to OPQR, then is congruent to __?__.
4-1
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
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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
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2. Given ΔABC ≌ ΔPQR, m∠B = 4v+1, and m∠Q = 8v-7, find m∠B and m∠Q.
4-1
Since ∠B corresponds to ∠Q
Plugging in 2
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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°
4-1
A. 5B. 57C. 4D. 3
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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°
4-1
A. 3 is the bottom side length and c is in the corresponding part so
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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
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4. Justify the last two steps of the proof.
4-2A. Reflexive Prop of ≌B. SSS
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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
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5. Name the angle included by the sides and .
4-2
N
P
M
∠N because it touches both of the listed sides.(Same letter in both sides is always the included angle.)
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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.
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6. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
4-2
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.
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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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4-3
7. What is the missing reason in the two-column proof?
D. ASA Postulate
ASA Postulate
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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
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8. Name the theorem or postulate that lets you immediately conclude ΔABD ≌ ΔCBD.
4-3
A
D
C
B
||
Reflexive
So ΔABD ≌ ΔCBD by SAS
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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
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9. Based on the given information, what can you conclude, and why?
4-3
1. Since because of vertical angles
2. by ASA
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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.
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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
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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 ≌
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11. Supply the missing reasons to complete the proof.
4-4
1. ASA2. Corres. parts of ≌
Δ are ≌
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12. Write a two-column proof.
4-4
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13. What is the value of x?
A. B. C. D.
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22%
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48°
Drawing not to scale
2121
xº
A. 66o
B. 71o
C. 132o
D. 142o
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13. What is the value of x?
4-5
48°
Drawing not to scale
2121
xº
Answer is A 66o
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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
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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
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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
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15. Find the values of x and y.
4-5
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
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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
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A
E
B
D
C
|
|
16. What additional information will allow you to prove the triangles congruent by the HL
Theorem?
4-6
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.
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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
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17. For which situation could you immediately prove Δ1 ≌ Δ2 using the HL Theorem?
4-6
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
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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
| |
A. Yes; ΔCAB≌ΔDAC.B. Yes; ΔACB≌ΔACD.C. Yes; ΔABC≌ΔACD.D. No, the triangles
cannot be proven congruent
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18. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?
4-6
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.
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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
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19. What common side do ΔCDE and ΔFED share?
4-7
A
G
E
B
D
H
C
F
They have side in common correct answer is A.
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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
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20. What common angle do ΔACF and ΔBCG?
4-7
C
G
AB
F They have angle ∠C in common correct answer is C.
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Chapter 4 Exam TOMORROW!
Journals due Friday
Portfolio Due Friday