Ch 1: The Essentials of Geometry

PRACTICE PROBLEMS

Assignment / Score / Learning Target(s) / Notes
What am I confident about?
Where do I need to spend more time?
Am I weak on a prerequisite skill?
What am I going to do if I am weak?
1.1 / 18
1.2 / 20
1.3 / 22
1.1-1.3 Review / 28
1.4 / 30
1.5 / 24
Ch Review / 20

Learning Targets:

Name and sketch geometric figures

Use segment postulates to identify congruent segments

Find lengths of segments in the coordinate plane

Name, measure, and classify angles

Use special angle relationships to find angle measures

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Unit 2 Syllabus: Ch 1Essentials of Geometry

Block / Date / Topic / Homework
7 / 9/22 / 1.1Identify Points, Lines, and Planes
1.2Use Segments and Congruence / Wkst: 1.1 Definitions and 1.2 Segment Addition Postulate
8 / 9/24 / 1.3 Use Midpoint and Distance Formulas / Wkst: 1.3 Midpoint and Distance
9 / 9/26 / Review Day / Wkst: 1.1-1.3 Review
10 / 9/30 / Quiz 1.1-1.3 / Spiral Review
11 / 10/2 / 1.4 Measure and Classify Angles / Wkst: 1.4 Angle Measurement
12 / 10/4 / 1.5 Describe Angle Pair Relationships / Wkst: 1.5 Angle Relationships
13 / 10/6 / Review Day / Wkst: Chapter 1 Review
14 / 10/8 / Chapter 1 Test / Spiral Review

***Syllabus subject to change due to weather, pep rallies, illness, etc

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HW: 1.1 Points, Lines, and Planes

In Exercises 1–6, use the diagram.

  1. Are points J, K, and L collinear or coplanar?
  1. Are points J, K, and M collinear or coplanar?
  1. Name the intersection ofand .
  1. Name the intersection of and plane KMN.
  1. Name the intersection of plane R and plane S.
  1. Name three pairs of opposite rays.

Use Diagram to left to answer questions 7-9

  1. Name 12 different rays.
  1. Name 2 pairs of opposite rays.
  1. Name 2 lines that intersect at point Z.

Using the appropriate labels sketch the following relationships.

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  1. intersects
  1. X is not on

  1. Points L, M, and N are collinear
  1. Points L, M, and N are noncollinear

  1. intersects plane Q at P
  1. Plane Q intersects plane R at

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HW: 1.2 Use Segments and Congruence


Find the indicated length.

HW: 1.3 Midpoint and Distance

Refer to the coordinate plane below to find the following.

16. The coordinates of A.

17. The coordinates of B.

18. The coordinates of C.

19. The coordinates of D.

20. The coordinates of E.

21. The distance from D to C. 22. The distance from E to A.

HW: Review 1.1-1.3

  1. In the diagram of collinear points, Find the length of each segment.

a. HI=_____

b. IJ=_____

c. GH=_____

d. JK=_____

e. IG=_____

f. IK=_____

Suppose J is between H and K. Use the Segment Addition Postulate to solve for x. Then find the length of each segment.

17. 18.

19. Determine if the following segments are congruent. Write a congruence statement if they are. Show all work to support and explain your answer.

: A(1,-3), B(0,5)

: C(1,1), D(-3,4)

20. Let E be a segment bisector of . Given FE= 8w-8, EG = 4w-4. Find the value of w.

21. The midpoint of is M(-6, 2). If the coordinates of point A are (4, 2), find the coordinates of the other endpoint, B.

Find the length of the segments with the given endpoints.

22. 23.

Find the midpoint of the segment with the given endpoints.

24. 25.

Given endpoint A and midpoint M of find the other endpoint.

26. 27.

28. Calculate to find which point A or B is farthest from the origin (0,0).

A(4, 3) or B(-1, 5)?

HW: 1.4 Angle Measurement

Write three names for the angle shown. Then name the vertex and the sides of the angle.

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1.

2.

3.

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Classify the angle with the given measure as acute, obtuse, right, or straight.

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4.

5.

6.

7.

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1

Give another name for the angle in the diagram. Tell whether the angle appears to be acute, obtuse, right, or straight.

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8. JKN

9. KMN

10. PQM

11. JML

12. QPN

13. PLK

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  1. List all of the angles have S as a vertex.
  2. Name a straight angle.
  3. Name an obtuse angle.
  4. Does SRU appear to be obtuse, right, acute, or straight?
  5. If the m3 =48 and m4 =23 then find the m RUT.
  6. If m6 is 177 the find m 2.

Find the indicated angle measure.

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1

Use the given information to find the indicated angle measure.

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24.

25.

26.

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In the diagram bisects ABC. Find mABC.

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27.

1

30.
28.

29.

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HW: 1.5 Angle Relationships

Using the figure below list all of the following that apply to each pair of angles: adjacent, vertical, complementary, supplementary, and linear pair.

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  1. 1 and2
  1. 1 and 4
  2. 4 and 5
  1. 1 and 5

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Use the figure below to answer questions 5-10

  1. Name one pair of complementary angles
  2. Name two angles that make a linear pair
  3. Name one pair of vertical angles.
  4. If m4=43◦, then find the m2.
  5. If m2=33◦, then find the m5.
  6. If m2=37◦, then find the m3.

Refer to the figure below and answer the following questions.

  1. If mABC =71◦, then find mCBD.
  2. If mDBC =23, then find the mCBA.
  3. If mABD = 2x-7, then find x.
  4. If mABC = 3x+12 and mCBD =x-8, then find x.
  1. If m1 is twice the measure of its complement (2), then determine the measure of each angle.
  1. If m3 is five times the measure of its supplement, then determine the measure of each angle.

Refer to the figure below and answer the following questions.

  1. If mABC =136, then find the mCBD.
  2. If mABC=7x-3 and mCBD =2x+12, then find x.

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  1. If mABC =119, then find mCBD.
  1. If mABC=5x+5 and mCBD=x+15, then find x.

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Find x and determine if . Explain why.

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Refer to the pictures below and find the missing angles.

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HW: Ch 1 Review

Use the diagram answer the following questions.

9.

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10. J is between H and K. Find the length of each segment using the following expressions.

HJ = 5x – 4

JK = 8x - 10

HK = 15x - 20
11.

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12. Given the endpoints of a segment, find the midpoint. A (6, -3) and B (10,5)

13. Given an endpoint and the midpoint of a segment, find the other endpoint. R (8,0), M(4,-5)

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14. Determine if the segments are congruent.

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15. Classify each angle as acute, obtuse, right or straight.

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16.

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1

1

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17. BD bisects ABC. Given that and find x.

18. Solve for x and y.

Show all equations and work!

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1

19. The following angles are complementary. Find their measures.

20. Tell whether the angles are vertical angles, a linear pair, or neither.

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