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GEOMETRY PRACTICE Test 2 (3.5-3.6)

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1. Find the value of the variable if 5. How many sides does a regular polygon have if and The diagram is each exterior angle measures 72? not to scale.

1 2 6. Find the missing angle measures. The diagram is l not to scale. 3 4

5 6 112° m x° 7 8 120° y° 79°

7. The jewelry box has the shape of a regular 2. The sum of the measures of two exterior angles of a pentagon. It is packaged in a rectangular box as triangle is 277. What is the measure of the third shown here. The box uses two pairs of congruent exterior angle? right triangles made of foam to fill its four corners. Find the measure of the foam angle marked.

SHOW ALL work to earn credit. 3. Find . The diagram is not to scale.

96°

118° 115°

x x

104° A

4. A nonregular hexagon has five exterior angle measures of 55, 58, 69, 57, and 55. What is the 8. Find the measures of an interior angle and an measure of the interior angle adjacent to the sixth exterior angle of a regular polygon with 6 sides. exterior angle? q

1 2 9. Write the equation 9x + 3y = –9 in slope-intercept p form. Then graph the line. 3 4

5 6 r 7 8

10. Write a two-column proof.

11. Find the measure of each interior and exterior angle Given: of the figure on the right. The diagram is not to scale. Prove:

11.

A. An equiangular polygon has all angles congrue 5 B. A regular polygon is both equilateral and 4 137 o equiangular. 6 C. An equilateral polygon has all sides congruent. D. A polygon is concave if no diagonal contains points outside the polygon.

1 2 8 9 3 7

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. . 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.

1 2 3 4 l

5 6 15. Write a two-column proof. 7 8 m

Given: are supplementary.

Prove:

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

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

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

22. Write an equation in point-slope form then write in 20. Complete this statement. A polygon whose sides all slope-intercept form of the line through point P(–4, have the same length is_____ 6) with slope –3. 29. Write a two-column proof? 23. Complete this statement. A polygon whose angles all have the same measure is ____. Given: and are supplementary.

24. At the curb a ramp is 13 inches off the ground. The Prove: other end of the ramp rests on the street 91 inches K straight out from the curb. A B J C D

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

26. Graph the line that goes through point (–2, 2) with 5  3 4 5 30. Graph y = x – 1. slope .

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

27. Write an equation in point-slope form, y – y1 = m(x – x ), of the line through points (5, –2) and (2, 10) 1 Use (5, –2) as the point (x , y ). 32. Write an equation for the vertical line that contains 1 1 point E(10, 1).

33. Write the equation for EACH graph 28. Write a two-column proof. a. y 6 Given: 4 Prove: and are supplementary. 2

–6 –4 –2 2 4 6 x a b –2 r c d –4 –6 e f s g h y b. 6 weeks)?

4 Estimate how long it would take for each of them 2 to have the same amount of money.

–6 –4 –2 2 4 6 x –2 –4 –6

c. y 6 4 2

–6 –4 –2 2 4 6 x –2 –4 –6

d. y 6 4 2

–6 –4 –2 2 4 6 x –2 –4 –6

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

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 Lines OBJ: 3-1.2 Properties of Parallel Lines STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0 TOP: 3-1 Example 5 KEY: corresponding angles | parallel lines | 2. ANS: 83

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 KEY: angle | triangle | exterior angle | Polygon Angle-Sum Theorem 3. ANS: 73

PTS: 1 DIF: L3 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 KEY: pentagon | exterior angle | sum of angles of a polygon 4. ANS: 114

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

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 TOP: 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 Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 TOP: 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 Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 TOP: 3-5 Example 5 KEY: angle | pentagon | Polygon Angle-Sum Theorem 8. ANS:

m (interior) = 120

m (exterior) = 60

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 KEY: Polygon Exterior Angle-Sum Theorem | exterior angle | interior angle 9. ANS: y = –3x – 3 y 6

–6 –4 –2 2 4 6 x –2

–4

–6

PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: 3-6.1 Graphing Lines TOP: 3-6 Example 3 KEY: slope-intercept form | point-slope form | graphing 10. ANS: a. Vertical angles. b. Transitive Property. c. Alternate Interior Angles Converse.

PTS: 1 DIF: L3 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.2 Using Exterior Angles of Triangles STA: CA GEOM 12.0| CA GEOM 13.0 KEY: 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 Plane OBJ: 3-6.2 Writing Equations of Lines KEY: 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 Theorems OBJ: 3-5.1 Classifying Polygons STA: CA GEOM 12.0| CA GEOM 13.0 KEY: classifying polygons | concave | convex | writing in math 14. ANS: D; a polygon is convex, not concave, if no diagonal contains point outsides the polygon.

ESSAY

15. ANS: [4]

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

c. 360 d.

This makes sense because an interior angle and its adjacent 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 Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 KEY: 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 Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 KEY: Polygon Exterior Angle-Sum Theorem 18. ANS: C PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: 3-6.1 Graphing Lines TOP: 3-6 Example 2 KEY: graphing | standard form of a linear equation 19. ANS: D PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 KEY: Polygon Angle-Sum Theorem 20. ANS: B PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 KEY: polygon | classifying polygons | equilateral 21. ANS: B PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 KEY: polygon | classifying polygons | equilateral 22. ANS: C PTS: 1 DIF: L3 REF: 3-6 Lines in the Coordinate Plane OBJ: 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 Theorems OBJ: 3-5.2 Polygon Angle Sums STA: CA GEOM 12.0| CA GEOM 13.0 KEY: polygon | classifying polygons | equilateral 24. ANS: B PTS: 1 DIF: L3 REF: 3-6 Lines in the Coordinate Plane OBJ: 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 Plane OBJ: 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 Plane OBJ: 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 Plane OBJ: 3-6.2 Writing Equations of Lines TOP: 3-6 Example 5 KEY: point-slope form 28. ANS: A PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel Lines OBJ: 3-1.2 Properties of Parallel Lines STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0 TOP: 3-1 Example 3 KEY: proof | two-column proof | supplementary angles | parallel lines | reasoning 29. ANS: A PTS: 1 DIF: L3 REF: 3-2 Proving Lines Parallel OBJ: 3-2.1 Using a Transversal STA: CA GEOM 2.0| CA GEOM 4.0| CA GEOM 7.0 TOP: 3-2 Example 1 KEY: parallel lines | reasoning | supplementary angles 30. ANS: A PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: 3-6.1 Graphing Lines TOP: 3-6 Example 1 KEY: slope-intercept form | graphing 31. ANS: D PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: 3-6.2 Writing Equations of Lines TOP: 3-6 Example 4 KEY: point-slope form 32. ANS: C PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: 3-6.2 Writing Equations of Lines TOP: 3-6 Example 6 KEY: vertical line 33. ANS: D PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: 3-6.1 Graphing Lines TOP: 3-6 Example 2

34.

35.