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Foundations Exam: Review SheetMs. Anderle

Foundations Exam:

Review Sheet

Plane Geometry: Multiple Choice Questions

1. Line j and k intersect at point P. Line m is drawn so that it is perpendicular to lines j and k at point P. Which statement is correct?

(1) Lines j and k are in perpendicular planes.

(2) Line m is in the same plane as lines j and k.

(3) Line m is parallel to the plane containing lines j and k.

(4) Line m is perpendicular to the plane containing lines j and k.

2. Through a given point, P on a plane, how many lines can be drawn perpendicular to that plane?

(1) 1(2) 2(3) more than 2(4) none

3. In plane P, lines m and n intersect at point A. In line k is perpendicular to linem and line n at point A, then line k is

(1) contained in plane P(3) skew to plane P

(2) perpendicular to plane P(4) parallel to plane P

4. In the diagram below, line k is perpendicular to plane P at point T.

Which statement is true?

(1) Any point in plane P also will be on line k.

(2) Only one line in plane P will intersect line k.

(3) All planes that intersect plane P will pass through T.

(4) Any plane containing line k will be perpendicular to plane P.

Free Response Questions: Answer each question below. Show all work.

  1. Two angles are supplementary. One angle is 30˚ more than another angle. Find both angles.
  2. Lines AB and CD intersect at E. If m<AEC = 6x – 27 and m<BEC = 8x + 11, find the measure of <BEC.
  3. <J and <A are vertical angles. If the m<J = 3x+20 and the m<A = 5x-50, then what is the value of <J?
  4. In the diagram below, m<ABC = 165˚. Find the value of x and m<CBD.
  5. In the diagram below, m<RPH = 112˚. Find the value of y and m<RPL.

  1. In the diagram below m||n. Using the diagram, find the value of x.
  2. In the diagram below m||n. Using the diagram, find the m<A.
  3. Find the value of r in the diagram below.
  4. In the diagram below form a straight angle. Using the diagram, find the m<DBC.

  1. bisects <CAT. m<CAB = 2x – 2 and m<BAT = x + 6. Find m<CAT.
  2. bisects right angle ABC. If the m<ABD is 6x – 3, then what is the value of x?
  3. What is the definition of perpendicular lines?
  4. Points F, G, and H lie on a line. The bisector of passes through G. What term is used to describe G?
  5. and are opposite rays. bisects <DEF. If m<KED is represented by
    10y – 5, what is the value of y?
  6. Can you measure a:
  7. line segment? ______
  8. line? ______
  9. ray? ______
  10. point? ______
  11. What do collinear points mean? Draw a picture of 3 points that are collinear.
  12. What is meant by exterior and interior points in an angle? Draw a picture where point M is on the exterior of <ABC and points R and K are on the interior of the angle.
  13. The measures of two complementary angles are in the ratio 1:4. What is the measure of the smaller angle?
  14. The measures of two supplementary angles are in the ratio 2:8. What is the measure of the larger angle?
  15. Point K is the midpoint of like TJ. If the length of JK = 2x – 4 and the length of
    TK = x + 6. what is the value of x? What is the length of segment TJ?