GEOMETRY PRACTICE Test 2 (3.5-3.6)

SHOW ALL WORK TO PROVE ANSWERS

1. Find the value of the variable if and The diagram is

not to scale.

1 23 4

5 67 8

l

m

2. The sum of the measures of two exterior angles of a triangle is 277. What is the measure of the third exterior angle?

3. Find . The diagram is not to scale.

A

96°

115°118°

104°

4. A nonregular hexagon has five exterior angle measures of 55, 58, 69, 57, and 55. What is the measure of the interior angle adjacent to the sixth exterior angle?

5. How many sides does a regular polygon have if each exterior angle measures 72?

6. Find the missing angle measures. The diagram is not to scale.

x°y°120° 79°

112°

7. The jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the foam angle marked.

SHOW ALL work to earn credit.

xx

8. Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides.

9. Write the equation 9x + 3y = –9 in slope-intercept form. Then graph the line.

10. Write a two-column proof.

Given: Prove:

1 23 4

5 67 8

q

p

r

11. Find the measure of each interior and exterior angle of the figure on the right.

The diagram is not to scale.

11.

5

4 137

6

2

3

18

7

9

o

12. Identify the form of the equation –3x – y = –2. To graph the equation, would you use the given form or change to another form? Explain.=

13.Explain how to tell whether a polygon is convex.

14.Which statement is false? Explain.

A. An equiangular polygon has all angles congrue B. A regular polygon is both equilateral and equiangular.C. An equilateral polygon has all sides congruent.

D. A polygon is concave if no diagonal contains points outside the polygon. .

15. Write a two-column proof.

Given: are supplementary.

Prove:

16. For a regular n-gon:a. What is the sum of the measures of its angles? b. What is the measure of each angle?c. What is the sum of the measures of its exterior angles, one at each vertex?d. What is the measure of each exterior angle.e. Find the sum of your answers to parts b and d. Explain why this sum makes sense.

l2

m

6

1

3 4

5

7 8

117. Complete this statement. The sum of the measures oof the exterior angles of an n-gon, one at each vertex, is ____.

18. Graph .

19. The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is ____.

20. Complete this statement. A polygon whose sides all have the same length is_____

21. Complete this statement. A polygon whose sides all have the same length and angles have the same measure is_____.

22. Write an equation in point-slope form then write in slope-intercept form of the line through point P(–4, 6) with slope –3.

23. Complete this statement. A polygon whose angles all have the same measure is ____.

24. At the curb a ramp is 13 inches off the ground. The other end of the ramp rests on the street 91 inches straight out from the curb.

25. Write an equation in slope-intercept form of the line through points S(–2, –6) and T(4, 3).

26. Graph the line that goes through point (–2, 2) with

slope 35 .

27. Write an equation in point-slope form, y – y1 = m(x – x1), of the line through points (5, –2) and (2, 10) Use (5, –2) as the point (x1, y1).

28. Write a two-column proof.

Given: Prove: and are supplementary.

a bc d

e fg h

r

s

29. Write a two-column proof?

Given: and are supplementary.Prove:

A BC D

E FG H

K

J

L

30. Graph y = 5

4x – 1.

31.Write an equation in point-slope form of the line through point K(–1, 6) with slope –4.

32.Write an equation for the vertical line that contains point E(10, 1).

33. Write the equation for EACH graph

a.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

b.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

c.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

d.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

34. Find the x- and y- intercepts for the following equation 5x – 8y = 40. Then graph.

35. Nancy and Jaime wanted buy their parents gifts for Christmas which was 2 months away. They both worked at Carl’s Jr. earning minimum wage. Nancy figured she could save $12 a week and she already had $52 in her piggy bank at home. Jaime decided to work extra hours and save $26 a week. Unfortunately he did have any money to start with.

Write equations and graph each situation. Which had more money saved in 2 months (8

weeks)?

Estimate how long it would take for each of them to have the same amount of money.

GEOMETRY PRACTICE Test 2 (3.5-3.6)Answer Section

SHORT ANSWER

1. ANS:–4

PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel LinesOBJ: 3-1.2 Properties of Parallel Lines STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0TOP: 3-1 Example 5 KEY: corresponding angles | parallel lines |

2. ANS:83

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: angle | triangle | exterior angle | Polygon Angle-Sum Theorem

3. ANS:73

PTS: 1 DIF: L3 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: pentagon | exterior angle | sum of angles of a polygon

4. ANS:114

PTS: 1 DIF: L3 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: hexagon | angle | exterior angle

5. ANS:5 sides

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0TOP: 3-5 Example 3 KEY: sum of angles of a polygon

6. ANS:x = 109, y = 60

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0TOP: 3-5 Example 4 KEY: exterior angle | Polygon Angle-Sum Theorem

7. ANS:72°

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0TOP: 3-5 Example 5 KEY: angle | pentagon | Polygon Angle-Sum Theorem

8. ANS:m (interior) = 120m (exterior) = 60

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: Polygon Exterior Angle-Sum Theorem | exterior angle | interior angle

9. ANS:y = –3x – 3

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.1 Graphing Lines TOP: 3-6 Example 3KEY: slope-intercept form | point-slope form | graphing

10. ANS:a. Vertical angles.b. Transitive Property.c. Alternate Interior Angles Converse.

PTS: 1 DIF: L2 REF: 3-2 Proving Lines ParallelOBJ: 3-2.1 Using a Transversal STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0TOP: 3-2 Example 1KEY: two-column proof | proof | reasoning | corresponding angles | multi-part question

11. ANS:

PTS: 1 DIF: L3 REF: 3-4 Parallel Lines and the Triangle Angle-Sum TheoremOBJ: 3-4.2 Using Exterior Angles of Triangles STA: CA GEOM 12.0| CA GEOM 13.0KEY: Triangle Angle-Sum Theorem | exterior angle

12. ANS:Standard form. Answer may vary. Sample: You could use the given form. Find the intercepts and use them to draw the line.

PTS: 1 DIF: L3 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.2 Writing Equations of LinesKEY: graphing | point-slope form | standard form of a linear equation | slope-intercept form | writing in math

OTHER

13. ANS:A polygon is convex if the points of all the diagonals are inside or on the polygon.

PTS: 1 DIF: L3 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.1 Classifying Polygons STA: CA GEOM 12.0| CA GEOM 13.0KEY: classifying polygons | concave | convex | writing in math

14. ANS:D; a polygon is convex, not concave, if no diagonal contains point outsides the polygon.

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: polygon | writing in math | reasoning | interior angle | Polygon Angle-Sum Theorem

ESSAY

15. ANS:[4]

[3] correct idea, some details inaccurate[2] correct idea, some statements missing[1] correct idea, several steps omitted

PTS: 1 DIF: L4 REF: 3-2 Proving Lines ParallelOBJ: 3-2.1 Using a Transversal STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0KEY: two-column proof | proof | extended response | rubric-based question | parallel lines | supplementary angles

16. ANS:[4] a. 180(n – 2)

b.

c. 360d.

e.

This makes sense because an interior angle and itsadjacent exterior angle are supplementary.

[3] parts a–d correct; small error in part e

[2] parts a–d correct

[1] three correct answers

PTS: 1 DIF: L4 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: exterior angle | Polygon Exterior Angle-Sum Theorem | extended response | rubric-based question

MULTIPLE CHOICE

17. ANS: B PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: Polygon Exterior Angle-Sum Theorem

18. ANS: C PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.1 Graphing Lines TOP: 3-6 Example 2KEY: graphing | standard form of a linear equation

19. ANS: D PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: Polygon Angle-Sum Theorem

20. ANS: B PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: polygon | classifying polygons | equilateral

21. ANS: B PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: polygon | classifying polygons | equilateral

22. ANS: C PTS: 1 DIF: L3 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.2 Writing Equations of Lines KEY: slope-intercept form

23. ANS: B PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0KEY: polygon | classifying polygons | equilateral

24. ANS: B PTS: 1 DIF: L3 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.2 Writing Equations of Lines KEY: word problem | problem solving | slope-intercept form

25. ANS: D PTS: 1 DIF: L3 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.2 Writing Equations of Lines KEY: slope-intercept form | slope

26. ANS: D PTS: 1 DIF: L3 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.2 Writing Equations of Lines KEY: graphing | slope-intercept form | slope | y-intercept

27. ANS: D PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.2 Writing Equations of Lines TOP: 3-6 Example 5KEY: point-slope form

28. ANS: A PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel LinesOBJ: 3-1.2 Properties of Parallel Lines STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0TOP: 3-1 Example 3KEY: proof | two-column proof | supplementary angles | parallel lines | reasoning

29. ANS: A PTS: 1 DIF: L3 REF: 3-2 Proving Lines ParallelOBJ: 3-2.1 Using a Transversal STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0TOP: 3-2 Example 1 KEY: parallel lines | reasoning | supplementary angles

30. ANS: A PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.1 Graphing Lines TOP: 3-6 Example 1KEY: slope-intercept form | graphing

31. ANS: D PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.2 Writing Equations of Lines TOP: 3-6 Example 4KEY: point-slope form

32. ANS: C PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.2 Writing Equations of Lines TOP: 3-6 Example 6KEY: vertical line

33. ANS: D PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate PlaneOBJ: 3-6.1 Graphing Lines TOP: 3-6 Example 2

34.

35.