Review&for&Quarter&2&test&&

1. An angle measures 10° less than the measure of its complementary angle. Find the measure of both angles. !!

2.!!A!triangle!has!vertices!at!A(−2,!3),!B(2,!1),!and!C(1,!0).!After!a!transformation,!the!image!of!the!triangle!has!vertices!at!!A"(−2,!−3),!B"(2,!−5),!and!C"(1,!−6).!Identify!the!transformation!!!!3.!Find!the!coordinates!of!the!midpoint!of!GH !with!endpoints!G(−7,!3)!and!H(5,!9).!!!4.!M!is!the!midpoint!of! ,RS !and!M!has!coordinates!(−1,!5).!R!has!coordinates!(−5,!2).!Find!the!coordinates!of!S.!!!!5.!Use!the!figure!for!Exercises!1–4.!

1. Name a point on line n. 2. Name a segment on line m.

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3. Name a ray with endpoint C. 4. Name three collinear points.

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6. R, S, and T are collinear, and S is between R and T. If RS = x + 1, ST = 2x − 2, and

RT = 5x − 5, find RT. A 2 C 5 B 3 D 6

7. Use the figure for Exercises a–d.

a. Which is a name for the plane containing point D?

A plane DB C plane EBD B plane P D plane FDE

b. Which segment is on plane P but is NOT on line n?

F BE H BC

G GB J AC

c. Name the intersection of plane P and line DE.

A Line GB C Point B B Point G D Line AC

d. Name the intersection of the two planes. F line n H line m

G point B J AC

8. Identify the property that justifies the statement “If ∠B ≅ ∠A, then ∠A ≅ ∠B.”

F Sym. Prop. of = G Reflex. Prop. of = H Trans. Prop. of ≅ J Sym. Prop. of ≅

9. What is the inverse of the conditional statement “If a number is divisible by 6, then it is divisible by 3”?

10. Write the converse of the conditional statement “If two angles are congruent, then they

have the same measure.”

11. What is the image of (5, 4) when it is rotated 180° about the origin? A (−5, −4) B (−4, 5) C (−5, 4) D (4, 5)

12. When the point (−3, 2) is reflected across the y-axis, what is the resulting image? A (−3, −2) B (3, −2)

C (2, −3 D (3, 2)

13. The composition of two reflections across parallel lines is equivalent to which type of transformation? A translation

B rotation 14. ΔRST is reflected across the y-axis, and then its image is reflected across the x-axis. Which

single transformation moves the triangle from its starting position to its final position?

15. Which represents a dilation with a scale factor of 12

?

A center Q; ABCD → EFGH B center H; EFGH → JKLH C center Q; EFGH → JKLH D center H; JKLH → EFGH

16. What are the coordinates of the image of (−3, 2) when the point is reflected across the line y = 4? A (−3, 4) B (−1, 6) C (6, −3) D (−3, 6)

17. ΔRST is the image of a triangle under a dilation centered at the origin with a scale factor of

−1 .2

Which point is a vertex of the preimage of ΔRST for this dilation?

F (−2, −1) G (−4, −8) H (2, −1) J (8, 4)

18. Rectangle KLMN is transformed by a dilation centered at the origin with a scale factor of 0.75. What is the perimeter of the image?

A 12 units B 18 units C 20 units D 18 units2

19. Use the figure for Exercises a and b.

a. Given r || s, what is the measure of ∠1?

A 55° B 125° b. Given r || s, which angle is supplementary to ∠3?

A ∠1 B ∠2

20. Which inequality is correct?

A x < 23 B x > 20

21. Which line is perpendicular to y = 2x + 4?

A y = 2x − 6 B = − +1 72

y x

22. Lines r and s are cut by a transversal so that ∠1 and ∠2 are same-side interior angles. If m∠1 = (8x + 40)° and m∠2 = (12x + 20)°, for what value of x is it true that r || s? A 6 C 30 B 10 D 60

23. Write the equation of the line through (0, 4) and (2, 0) in slope-intercept form.

24. Write an equation in slope-intercept form for the line that passes through (6, 6) and is perpendicular to −2x + 3y = −6.

25. Write the equation of the perpendicular bisector of the segment with the end points

a) (2,5) and (4,9)

b) (1,3) and (-1,4)

26. Find the value of angle 1

a) b)

27.

!!!!28.!!

!!29.!

!!30.!

!!31.!Find!the!slope!of!line!parallel!and!perpendicular!to!the!!line!through!(−1,!8)!and!(4,!18).!!!!

32.!Which!line!is!perpendicular!to! = +y x1 52

?!

A = −y x1 72

C y = x + 10

B y = −2x + 5 D y = 2x + 10 33. a)Name angle that forms a linear pair with ∠MPS

b) Name angle that forms a vertical angle pair with ∠MPS c) Give a relationship between ∠MPR, ∠RPK,!∠KPN

!

34. What is the length of side BC?

A 3 C 10 B 8 D 24

35. Describe the transformation M: (x, y) → (-y, x).

A A reflection across the y-axis. B A reflection across the x-axis. C A rotation 90° clockwise with center of rotation (0, 0). D A rotation 90° counterclockwise with center of rotation (0, 0).

36. Find the value of x.

37. Find the measure of ∠RST.

38. If ΔKMQ ≅ ΔWJR, which segment is congruent to RW ?

A KM C QK

B MQ D JW 39. Find the value of x.

!

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&&&&&&11.#Solve#the#system#by#substitution#

y = -3x + 53

y = 6 - 2x 12.

13.

14.

15.