answer key_ck-12 chapter 04 basic geometry concepts

8/15/2019 Answer Key_CK-12 Chapter 04 Basic Geometry Concepts

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4.1 Triangle Sum Theorem

Answers

1. m!1 = 41°

2. m!1 = 86°

3. m!1 = 61°

4. m!1 = 51°

5. m!1 = 13°

6. m!1 = 60°

7. m!1 = 70°

8. 84°

9. 57°

10. 21°

11. x = 14°

12. x = 9°

13. x = 22°

14. x = 17°

15. x = 12°


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4.2 Exterior Angles Theorem

Answers

1. m!1 = 118°

2. m!1 = 68°

3. m!1 = 116°

4. m!1 = 161°

5. m!1 = 141°

6. m!1 = 135°

7. 180°

8. 360°

9. 360°

10. x = 30°

11. x = 25°

12. x = 7°


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4.3 Congruent Triangles

Answers

1. Yes

2. Yes

3. Yes

4. No

5. No

6. Yes

7. No

8. Yes

9. No

10. Yes

11. No

12. Yes

13. Yes

14. No

15. No


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4.4 Congruence Statements

Answers

1. "FGH # "KLM

2. No, we do not know if !" ! !", so we cannot say that the triangles are congruent.

3. " ABE # "DCE

4. No, we only know that one pair of sides and one pair of angles are congruent. This is

not enough information to determine if the triangles are congruent.

5. Line up the congruent sides: "BCD # "ZYX

6. Corresponding Parts of Congruent Triangles are Congruent or CPCTC.

7. !T # !F , !B # ! A, !S # !M , ! ! !, ,TB FA BS AM TS FM

8. !P # !S, ! A # !T , !M # !E , ! ! !, ,PA ST AM TE PM SE

9. !I # !W , !N # !E , !T # !B, ! ! !, ,IN WE NT EB IT WB

10. !E


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4.5 Third Angle Theorem

Answers

1. 88°

2. 42°

3. 50°

4. 42°

5. 47°

6. 43°

7. 47°

8. 37°

9. Lines are not marked parallel, we cannot assume that m!HIJ = 108°.

10. 35°

11. Lines are not marked parallel, we cannot assume that m!IHJ = 37°.

12. 55°

13. 63°

14. 62°

15. 63°


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4.6 SSS Triangle Congruence

Answers

1. Yes, "DEF # "HJI , SSS

2. No, one triangle is SSS and the other is SAS.

3. Yes, " ABC # "FED, SSS

4. Yes, " ATD # "ETD, SSS

5. AB HI !

6. AB JL!

7.

Statement Reason

1. B is the midpoint of DC ,Given

2. DB BC ! Definition of a Midpoint

3. Reflexive PoC

4. " ABD # " ABC SSS

8. Triangle #1: (-8, 0), (0, 3), and (-5, 9), Side #1 ! !", Side #2 ! !", Side #3 ! !"

Triangle #2: (2, 5), (10, 2), and (5, -4), Side #1 ! !", Side #2 ! !", Side #3 ! !"

The triangles are congruent by SSS.

AD AC !

AB AB!


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9. Triangle #1: (-7, 2), (1, 6), and (4, 5), Side #1 ! !", Side #2 ! !"#, Side #3 ! !"

Triangle #2: (-1, -10), (-5, -2), and (-8, -1), Side #1 ! !", Side #2 ! !"#, Side #3

! !"


10. " ABC : AB ! !", AC ! !", BC ! !", "DEF : DF ! !", DE ! !", EF ! !"#

The triangles are not congruent because not all the corresponding sides are congruent.

11. " ABC : AB ! !", AC ! !", BC ! !", "DEF : DE ! !" ,DF ! !", EF ! !"



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4.7 SAS Triangle Congruence

Answers

1. No, these are both SSA, which is not a congruence postulate.

2. Yes, " ABC # "YXZ , SAS

3. No, these are both SSA, which is not a congruent postulate

4. !C # !G

5. !C # !K

6. AB ON !

7.

Statement Reason

1. B is a midpoint of DC , AB DC ! Given

2. DB BC ! Definition of a midpoint

3. ! ABD and ! ABC are right angles $ lines create 4 right angles

4. ! ABD # ! ABC All right angles are #

5.Reflexive PoC

6. " ABD # " ABC SAS

AB AB!


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8.

Statement Reason

1. AB is an angle bisector of !DAC ,Given

2. !DAB # !BAC Definition of an Angle Bisector

3. Reflexive PoC

4. " ABD # " ABC SAS

9.

Statement Reason

1. B is the midpoint of DE and AC ,

! ABE is a right angle

Given

2. ,DB BE AB BC ! ! Definition of a Midpoint

3. m! ABE = 90° Definition of a Right Angle

4. m! ABE = m!DBC Vertical Angle Theorem

5. " ABE # "CBD SAS

10.

Statement Reason

1. DB is the angle bisector of ! ADC , AD DC ! Given

2. ! ADB # !BDC Definition of an Angle Bisector

3. DB DB! Reflexive PoC

4. " ABD # "CBD SAS

AD AC !

AB AB!


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4.8 ASA and AAS Triangle Congruence

Answers

1. Yes, AAS, " ABC # FDE

2. Yes, ASA, " ABC # "IHG

3. No, the triangles have congruent parts that would be SSA. This is not a congruence

theorem.

4. !DBC # !DBA because they are both right angles and created by perpendicular lines.

5. !CDB # ! ADB

6. !" ! !" from the Reflexive Property. We have enough to say that the triangles are

congruent by ASA.

7.

Statement Reason

1. DB AC ! ,

DB is the angle bisector of !CDA

Given

2. !DBC and ! ADB are right angles Definition of perpendicular

3. !DBC # ! ADB All right angles are #

4. !CDB # ! ADB Definition of an angle bisector

5. DB DB! Reflexive PoC

6. "CDB # " ADB ASA


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8. !C # ! A by CPCTC (corresponding parts of congruent triangles are congruent)

9. !L # !O and !P # !N by the Alternate Interior Angles Theorem.

10. !LMP # !NMO by the Vertical Angles Theorem.

11. There is more than one correct proof, this is one possible answer.

Statement Reason

1. ||LP NO , LP NO! Given

2. !L # !O, !P # !N Alternate Interior Angles Theorem

3. "LMP # !OMN ASA

12. CPCTC

13. Start with the proof from #11 and continue.

Statement Reason

1. ||LP NO , LP NO! Given

2. !L # !O, !P # !N Alternate Interior Angles

3. "LMP # !OMN ASA

4. LM MO! CPCTC

5. M is the midpoint of PN . Definition of a midpoint

14. ! A # !N

15. !C # !M

16. PM MN !

17. !" ! !" or !" ! !"


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4.9 HL Triangle Congruence

Answers

1. !NM ZX

2. ! !orFG RS FE RQ

3. ! ! !and orVW DC WX CB VX DB

4. Given/Definition of Perpendicular Lines

5. ! AC CD

6. !ED AB

7. HL Congruence

8. No

9. Yes, by SAS

10. No

11. Yes, by HL

12. No

13. No

14. Yes, by SSS

15. No


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4.10 Isosceles Triangles

Answers

1. x = 13°

2. y = 16°

3. x = 1

4. y = 3

5. x = 4°, y = 11°

6. True

7. False, only in an isosceles right triangle.

8. False, only in the case of an equilateral triangle.

9. True

10.

Statement Reason

1. Isosceles "CIS, with base angles !C and

!S IO is the angle bisector of !CIS

Given

2. !C # !S Base Angles Theorem

3. !CIO # !SIO Definition of an Angle Bisector

4. IO# IO Reflexive PoC

5. "CIO # "SIO ASA

6. CO OS ! CPCTC

7. !IOC # !IOS CPCTC

8. !IOC and !IOS are supplementary Linear Pair Postulate

9. m!IOC = m!IOS = 90° Congruent Supplements Theorem

10. IO is the perpendicular bisector of CS Definition of a $ bisector (Steps 6 and 9)


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11.

Statement Reason

1. Isosceles "ICS with !C and !S, IO is the

perpendicular bisector of CS

Given

2. !C # !S Base Angle Theorem

3. CO OS ! Definition of a $ bisector

4. m!IOC = m!IOS = 90° Definition of a $ bisector

5. "CIO # "SIO ASA

6. !CIO # !SIO CPCTC

7. IO is the angle bisector of !CIS Definition of an Angle Bisector

12. Side #1 = !", Side #2 = !", Side #3 = !

This is an isosceles triangle because Side #1 and Side #2 are equal.

13. Side #1 = !", Side #2 = !", Side #3 = !

No sides are equal, so this is a scalene triangle.

14. Side #1 = !", Side #2 = !"#, Side #3 = !"#

No sides are equal, so this is a scalene triangle.

15. Side #1 = !"#, Side #2 = !"#, Side #3 = !"#


16. Side #1 = !, Side #2 = !", Side #3 = !"



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4.11 Equilateral Triangles

Answers

1. x = 60°

2. y = 68°

3. x = 1.5

4. y = 17

5. z = 17

6. n = 25°

7. = ±4 2 x

8. x = 3, y = 2

9. x = 2, y = 5

10. z = 4

11. a = !1, 6

12. m = !4°, 15°

13. x = 4, !1

14. = ±2 14 x

15. x = 25°, y = 19°

answer key_ck-12 chapter 04 basic geometry concepts

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