0005_hsm11gmtr_0401.indd



CHAPTER 4 HOMEWORK PACKET

Subject: Geometry

This packet must be completed and returned before or on the day of the Chapter 1 Test. ALL WORK MUST BE SHOWN WHEN POSSIBLE. ANSWERS WITH NO WORK WILL NOT BE ACCEPTED. If extra space is needed please staple papers to this packet and turn everything in at the same time.

NAME: ___________________________________________________

Grade: ____________________ / 87

Homework Section 1

Each pair of polygons is congruent. Find the measures of the numbered angles.

1. 2.

Use the diagram at the right for Exercises 3–7. (ABC ( (XYZ. Complete the congruence statements.

3. [pic] (

4. [pic] (

5. (BAC (

For Exercises 10 and 11, can you conclude that the figures are congruent? Justify your answers.

6. (SRT and (PRQ 7. (ABC and (FGH

8-11 Given: [pic] and [pic] bisect each other.

[pic] ( [pic]; (A ( (D

Prove: (ACB ( (DCE

|Statements |Reasons |

|[pic] and [pic] bisect each other. |Given |

|[pic] ( [pic], (A ( (D | |

|[pic] ( [pic], [pic] ( [pic] |8) |

|(ACB ( (DCE |9) |

|(B ( (E |10) |

|(ACB ( (DCE |11) |

Algebra Find the values of the variables.

12. (XYZ ( (FED 13. (ABD ( (CDB

Algebra (FGH ( (QRS. Find the measures of the given angles or the lengths of the given sides.

14. m(F = x + 24; m(Q = 3x 15. [pic] = 3x ( 2; [pic] = x + 6

Homework Section 2

List the pairs of congruent, corresponding parts you already know.

Then tell what other information, if any, do you need to prove the two triangles

congruent by SAS?

1. 2.

Would you use SSS or SAS to prove these triangles congruent? If there is not enough information to prove the triangles congruent by SSS or SAS, write not enough information. Explain your answer.

5. 6.

Use the Distance Formula to determine whether ∆FGH and ∆JKL are congruent. Justify your answer.

7. F((2, 5), G(4, (3), H(4, 3), J(2, 1), K((6, 7), L((6, 1)

Can you prove the triangles congruent? If so, write the congruence statement

and name the postulate you would use. If not, write not enough information and tell what other information you would need.

8. 9.

10-15 Given: [pic] is the perpendicular bisector of [pic].

Prove: ∆BAD ( ∆BCD

|Statements |Reasons |

|[pic] is the perpendicular bisector of [pic]. |Given |

|[pic] |Definition of segment bisector |

| | |

|(ADB and (CDB are right [pic]. |Definition of perpendicular |

| | |

|10) |11) |

| | |

|12) |13) |

| | |

|14) |15) |

Homework Section 3

Name the two triangles that are congruent by ASA.

1. 2.

3-7 Developing Proof Complete the two-column proof by filling in the blanks.

Given: [pic] bisects (ABC

Prove: ∆ABD ( ∆CBD

|Statements |Reasons |

|[pic] bisects (ABC |Given |

|3) |Definition of perpendicular |

|(ADB ( (CDB |4) |

|(ABD ( (CBD |5) |

|6) |Reflexive Property of ( |

|7) |ASA |

8-10 Given: [pic](KJL ( (MNL

Prove: ∆JKL ( ∆NML

|Statements |Reasons |

|[pic](KJL ( (MNL |Given |

|(KLJ ( (MLN |8) |

|9) |Third Angles Theorem |

|10) |ASA |

11-15 Given: [pic] is the angle bisector of (ABC and (ADC.

Prove: ∆ABD ( ∆CBD

|Statements | Reasons |

|11) |Given |

|12) |Definition of ( bisector |

|(BAD ( (BCD |13) |

|[pic] |14) |

|15) |AAS |

Homework Section 4

1. Developing Proof State why the two triangles are congruent. Then list all other corresponding parts

of the triangles that are congruent.

2-6 Given: [pic](R ( (S

Prove: (QTS ( (TQR

|Statements |Reasons |

|2) |Given |

|3) |Alternate interior [pic] are (. |

|4) |Reflexive Property of Congruence |

|5) |AAS |

|6) |Corresp. parts of ( [pic] are (. |

7. Given: [pic] is the perpendicular bisector of [pic].

Prove: [pic] ( [pic]

|Statements |Reasons |

|[pic] is the perpendicular bisector of [pic]. |Given |

|7) |2) Def. of perpendicular bis. |

|(GKF ( (GKH |Def. of perpendicular bis; all right [pic] are (. |

|8) |Refl. Prop. of ( |

|∆FGK ( ∆HGK |9) |

|10) |Corresp. parts of ( [pic] are (. |

11-15 Given: ABCE is a rectangle.

D is the midpoint of[pic].

Prove: [pic]

|Statements |Reasons |

|ABCE is a rectangle. D is the midpoint of [pic]. |Given |

|(AED ( (BCD |Definition of rectangle |

|[pic] ( [pic] |Definition of rectangle |

|11) |12) |

|13) |14) |

|[pic] |15) |

Homework Section 5

Complete each statement. Explain why it is true.

1. [pic] (

2. (CBE ( ( (BCE

Algebra Find the values of x and y.

3. 4.

5. You are asked to put a V-shaped roof on a house. The slope of the roof is 40°. What is the measure of the angle needed at the vertex of the roof?

6. Reasoning The measure of one angle of a triangle is 30. Of the two remaining angles, the larger angle is four times the size of the smaller angle. Is the

triangle isosceles? Explain.

For Exercises 7 and 8, use the diagram to complete each congruence statement. Then list the theorem or corollary that proves the statement.

7. [pic] (

8. (E (

11.

For Exercises 9–11, use the diagram to complete each congruence statement. Then list the theorem or corollary that proves the statement.

9. [pic] (

10. (RUV (

11. [pic] (

Algebra Find the values of m and n.

12.

Homework Section 6

1-4 Developing Proof Complete the proof.

Given: (WVZ and (VWX are right angles.

[pic]

Prove: (WVZ ( (VWX

.

|Statements |Reasons |

|1) |1) Given |

|2) |2) Given |

|3) |3) Reflexive Property of Congruence |

|4) |4) HL Theorem |

5. Look at Exercise 1. If m(X = 54, what is m(Z?

6. Look at Exercise 1. If m(X = 54, what is m(VWZ?

Algebra For what values of x and y are the triangles congruent by HL?

7. 8.

Form K

What additional information would prove each pair of triangles congruent by the Hypotenuse-Leg Theorem?

10. 11.

12. 13.

14-15 Complete the paragraph proof below that shows that (ACD ( (DBA.

(ACD is a from Exercise 12. You can also use the product of slopes to show that (ABD is a right angle. (ACD and (ABD share the same hypotenuse. You can use the to show that AB = CD. Therefore, by the , (ACD ( (DBA.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download