120˚ y˚

2013-2014Geometry

First Nine Weeks Study Guide

1. What is the value of y?

2. The figure shows two lines that intersecting at point B.

What is the m∠ ABD?

3. A supporting beam for a porch forms two angles with a vertical beam in the outside wall where the porch is attached to the house. What is the measure of the larger angle formed by the support and the vertical beam?

4. What is the measure of a complement of a 48o angle?5. Angle 1 is t he supplement of angle 2. If the m ∠1 =3x+16 and the m ∠2 =x+2, Find the value of angle 2.

6. What is the slope of the line parallel to the line that pass through the points (6, 1) and (–4, –5)?

7. Determine in the lines 3x – 2y = 5 and 6x + 4y = -16 are parallel, perpendicular, or neither.8. What are the coordinates of the midpoint of the segment with endpoints C(10, –8) and D(2, 6)?

9. If m 2 = 48 and m 6 = 48, which statement is true?

a. a is parallel to b because all vertical angles are congruent.b. a is parallel to b because corresponding angles are congruent.c. a is parallel to b because interior angles on the same side of the transversal are congruent.d. a is not parallel to b.

10. If m 1 = 2x + y, m 2 = 9x + 6y + 28, and m 3 = 12x + 8y 14, for what value of x will line m be parallel to line n?

11. What is the slope of a line perpendicular to a line with slope 23?

12. Tell which statement is the contrapositive of the statement If Juan is watching military drills, then Juan is in Williamsburg.a. Juan is not in Williamsburg.b. If Juan is not watching military drills, then Juan is not in Williamsburg.c. If Juan is not in Williamsburg, the Juan is not watching military drills.d. If Juan is in Williamsburg, then Juan is watching military drills.

13. If it is Saturday, then I will wash my car. If I wash my car, I will go to town.

What conclusion will logically follow the true statements?

Which law will you use?

14. Twenty students were asked what they did over the weekend. The results are shown in this Venn diagram.

a. How many of the students saw a movie and went to a concert?

b. How many of the students went to a concert?

15. Which argument has the same form as this symbolic argument?

Assume: p or q ~pConclude:

q

a. I go to school or I go to work. If I do not go to school, then I go to work.

b. If I go to school, then I go to work. I do not go to school. Therefore, I do not go to work.

c. I go to school or I go to work. I do not go to school. Therefore, I go to work.d. I go to school and I go to work. I do not go to school. Therefore, I go to work.

16. What statement follows from the two statements given below?All guinea pigs have four legs.Squirt is a guinea pig.

a. Squirt does not have four legs. c. Squirt has four legs.

b.

Squirt is not a guinea pig. d. Guinea pigs do not have four legs.

Which law justifies this?

17.

What conclusion follows from the two statements given below?If it is raining, then I carry my umbrella. I am not carrying my umbrella.

a. It is not raining.b. It is raining.c. I carry my umbrella.d. If it is not raining, then I do not carry my umbrella.

18. What is the distance between the points at (2, 3) and (6, -6)?

19. What is being constructed in this figure?

a. the perpendicular bisector of line mb. the line perpendicular to line m through a point on the linec. the line parallel to line m through a point not on the lined. an angle that has line m as its bisector

20. In the figure j||k. What is the value of x?

x° z°52°

98°

21.

The drawing shows the arcs used to construct

a. A copy of a segmentb. A bisector of a segmentc. A bisector of a angled. A copy of a angle

22.

The drawing shows the arcs used to construct

a. A copy of a segmentb. A bisector of a segmentc. A bisector of a angled. A copy of a angle

23.

Find the values of x and z.

24.

Find the distance and the midpoint of the two points.

25.

26. Identify the center and radius of each. Then sketch the graph.

(x – 1)² + (y + 3)² = 4

27. Write the equation of a circle with a center at (-3, -6) and passes through the point (-4, 8).

28. Write the equation of the circle whose graph is shown below.

29. Given with a diameter of CD

passing through point R given the endpoints C (6, 2) and D (-8, 2). Write the standard form of the equation of the circle.

30. State the equation of a circle which has a center at (5, -3) and a radius of 9.

Technology Enhanced Items:

31. Line m contains the points (1, 2) and (-4, -7). Plot a point other than point P (-4, 3) with integral coordinates that lie on a line that is parallel to m and passes through point P.

1 2 3 4 5 6 7 8 9 10–1–2–3–4–5–6–7–8–9–10 x

123456789

10

–1–2–3–4–5–6–7–8–9

–10

y

Directions: Plot a point on the grid. You must plot a point other than P.

P

(3, -1)

(-1, -1)

(5, -2)

(6, 1)

(0, 0)

32. Circle O is defined by the equation (x – 3)2 + y2 = 36. Plot the center of circle O and two points for the endpoints of the diameter of circle O on the coordinate plane.

33. Given: Circle K K (1, -2) Radius = 5 units

Which points lie on circle K?

Directions: Plot three points on the correct spot on the coordinate grid.

Directions: Circle the box to choose each point you want to select. You must select all correct points.

34. Line m and line n are parallel. The measure of 1 is 82o. Find the measure of 2, 6, and 7.

2 =

6 =

7 =

35. The Venn diagram below shows the enrollment in several courses for a group of high school freshman. Put a star in the section that represents the following statement.

“Some freshman students take geometry and earth science but do not take world history.”

Directions: Fill in the answer in the place provided.

Directions: Place a star in the correct region(s).

Freshman

GeometryWorld History

Earth Science