1. On the number line shown, point T has coordinate -15 and point M has coordinate -27. If point T is the midpoint of , what is the coordinate of point A?
______
In 2 and 3, use the figure shown, in which r // s.
2. Suppose that m5 = 33.
- Find m 1.______
- Find m2.______
3. Suppose that m2 = 13n – 9 and m4 = 7n – 3. Find m3.______
4. In the figure shown, I is the midpoint of , NB = 11x + 3, and NI = 3x + 9. Find NB.
______
5. Can the numbers 10.5, 11, and 30 be the side lengths of a triangle?______
6. Point X is between point Z and point W. If XZ = 7 and XW = 19, find WZ.______
7. In the figure shown, bisects AMB, mAML = 6s, and mBML = s + 20.
- FFind s. ______
- FFind mAMB. ______
8. Identify the figure that shows a counterexample to the following statement: If two angles are complementary, then they are adjacent. ______
9. In coordinate geometry, the graph of the line with equation y = -400 is a(n) ______line.
a) horizontal b) vertical c) oblique d) drum
10. On a number line, AT = 40 and the coordinate of A is -5. What are the possible coordinates of T?
a) -45 only b) 35 only c) -45 or 35 d) -35 or 45
11. Consider the conditional: I’ll take my umbrella if it looks like rain. Which statement is the converse of this conditional?______
a) If it looks like rain, I’ll take my umbrella.
b) If I take my umbrella, then it looks like rain.
c) If it doesn’t look like rain, then I’ll take my umbrella.
d) If I take my umbrella, then it doesn’t look like rain.
12. Two angles are supplementary. The measure of the larger angle is 6j and the measure of the smaller is 2j. What are the measures of the two angles? ______
a) 22.5 and 135
b) 45 and 135
c) 22.5 and 67.5
d) cannot be determined
13. Let P = (-3, -5) and R = (2, -7). What is the slope of ?______
a) b) c) d)
14. The slope of any line perpendicular to the line with equation -2x + 3y = 9 is ______.
a) b) c) d)
15. Give the slope of the line through (-4, -7) and (-1, 5). ______
16. True or False. Any line perpendicular to the line with equation 3x + y = 7 must have slope .
17. Use the figure shown in which m // n. If m4 = 33, then m7 = ____.
a) 57 b) 157 c) 147 d) none of these
18. In the figure shown, is the bisector of AMT and is the bisector of RMB. If mAMT = 88, then mRMB = ______.
a) 44 b) 132 c) 90 d) 88
In 19 and 20, use the figure shown, in which j // k.
19. If m6 = 84, find m4.______
20. Suppose that m8 = 8w + 12 and m6 = 10w – 6.
a. Find w. ______
b. Find m4. ______
In 21 – 22, MNO shown is isosceles with base .
21. If mM = 96, find mN. ______
22. If mN = 7k and mO = 20 + 2k, find k: ______and mM: ______.
23. In the figure shown, find z: ______and mE: ______.
24. In the figure shown, N is the midpoint of . If RN = 20 – 3x and NT = x + 4, then RT = ______.
a) 16b) 12c) 8d) 4
25. In TOP at the right, mO = ______.
a)85b) 59c) 36d) 17
26. In the figure shown, (A B; ) find mA.
a) 148b) 138c) 119d) 28
27. Which is the most specific name possible for the figure shown?
a)trapezoidb) parallelogramc) rectangle
d) isosceles trapezoid
28. In the figure shown, is the bisector of . SL = 20g, and ML = 15g. What is MS?
a)7.5gb) 10gc) 15gd) 20g
29.MNO shown is isosceles with base . The measure of
N is three times the measure of O. What is the measure of N?
a)36b) 72c) 108d) 135
30. Give the slope of the line through (-7, 15) and (2, 10).______
31. Write an argument for this proof.
Given:
Prove:
StatementsReasons
32. Refer to parallelogram PARL shown. Let PA = 4 and RT = 2.8.
a)What other segments have length 4? ______
b)What other segments have length 2.8? ______
33. Write an argument for this proof.
Given:
Prove:
Statements Reasons
34. In the figure shown, p // q. If m1 = 2y + 25 and m2 = 3y – 20, findm3: ______.
35.If , and , find the degree measure of The diagram is not to scale.
36.In the figure shown, . Which of the following statements is false?
(Not drawn to scale)
a. /b. / BEC and CED are adjacent angles.
c. /
d. / AED and BEC are adjacent angles.
37. and are a linear pair. , and . Find the measure of each angle.
38.Find the midpoint of
a. / (2, 0) / b. / (2, 1) / c. / (1, 1) / d. / (1, 0)39.Rewrite the following conditional and its converse as a biconditional statement.
If an angle is a right angle, its measure is 90.
If an angle measure is 90, the angle is a right angle.
40.Use the Law of Transitivity to draw a conclusion from the two given statements.
If you exercise regularly, then you have a healthy body.
If you have a healthy body, then you have more energy.
a. / You have more energy.b. / If you do not have more energy, then you do not exercise regularly.
c. / If you exercise regularly, then you have more energy.
d. / You have a healthy body.
41.Write an equation in point-slope form of the line through point J(–5, 6) with slope –4.
a. / / c. /b. / / d. /
42.Write the equation for the horizontal line that contains point G(4, 8).
a. / y = 4 / b. / y = 8 / c. / x = 8 / d. / x = 443.What is an equation in point-slope form for the line perpendicular to y = 3x + 9 that contains (–6, 5)?
a. / x – 5 = 3(y + 6) / c. / y – 6 = (x + 5)b. / y – 5 = (x + 6) / d. / y – 5 = 3(x + 6)
44.Find the value of x. The diagram is not to scale.
45.If , which of the following can you NOT conclude as being true?
a. / / b. / / c. / / d. /46.What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate?
47.State whether and are congruent. Justify your answer.
a. / yes, by either SSS or SASb. / yes, by SSS only
c. / yes, by SAS only
d. / No; there is not enough information to conclude that the triangles are congruent.
48.Name the theorem or postulate that lets you immediately conclude
a. / AAS / b. / SAS / c. / ASA / d. / none of these49.Based on the given information, what can you conclude, and why?
Given:
a. / by ASA / c. / by ASAb. / by SAS / d. / by SAS
50.Given: and
Prove:
51.Two sides of an equilateral triangle have lengths and . Which could be the length of the third side: or ?
52.For which situation could you immediately prove using the HL Theorem?
53.Given:,
Prove:
54.Find the value of x.
55.Which statement is not necessarily true?
Given: is the bisector of
a. / DK = KE / c. / K is the midpoint of .b. / / d. / DJ = DL
56. bisects Find the value of x. The diagram is not to scale.
57.Find the circumcenter of the triangle.
58.In ACE,G is the centroid and BE = 9. Find BG and GE.
a. / BG = , GE = / c. /b. / / d. / BG = , GE =
59.What is the name of the segment inside the large triangle?
a. / altitude / c. / angle bisectorb. / perpendicular bisector / d. / median
60.List the sides in order from shortest to longest. The diagram is not to scale.
61.Two sides of a triangle have lengths 7 and 15. Write an inequality that represent the possible lengths for the third sidex.
62.Find the sum of the measures of the angles of the figure.
a. / 900 / b. / 1080 / c. / 1620 / d. / 126063.What is the measure of one angle in a regular 25-gon?
a. / 194.4 / b. / 4140 / c. / 165.6 / d. / 82.864.How many sides does a regular polygon have if each exterior angle measures 20?
a. / 17 sides / b. / 20 sides / c. / 21 sides / d. / 18 sides65.Find the values of the variables in the parallelogram. The diagram is not to scale.
a. / / c. /b. / / d. /
66.In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 4x – 5, and HE = 2y + 3. Find the values of x and y. The diagram is not to scale.
a. / x = 6, y = 3 / b. / x = 2, y = 3 / c. / x = 3, y = 2 / d. / x = 3, y = 667.Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain.
a. / Yes; both pairs of opposite sides are congruent.b. / Yes; opposite angles are congruent.
c. / No; you cannot prove that the quadrilateral is a parallelogram.
d. / Yes; two opposite sides are both parallel and congruent.
68.If possible, write a congruence statement for each pair of triangles. Then name the triangle-congruence postulate that applies. If the triangles are not congruent, say so.
69. In the figure below, Q and Z are the midpoints of their respective sides.
a. What do we call ?
b. Solve for x and AC:
c. The and . What is
70. Given: is a perpendicular bisector of . Find the measure of BAD.