1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?


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1 1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width of the compass is more than half the distance between the two points. Step 3: Without changing the compass width, draw an arc on each side of the line segment. Step 4: Without changing the compass width, repeat the process from Step 3 on the other endpoint of the line segment, making sure that the two new arcs intersect the first two arcs that were constructed. Step 5: Plot a point on the intersection of the two arcs on each side of the line segment. Step 6: Use a straightedge to draw a line between the two points. Which type of construction is best represented by the steps given above? A. perpendicular bisector of a line segment B. angle congruent to a given angle C. parallel line through a point not on the given line D. bisector of an angle
2 2. If T is the midpoint of and V lies between R and T, which statement must be true? A. B. C. D. 3. Duplicating an angle can be accomplished using a compass and a straightedge. An example of duplicating Angle PQR is shown below. How many of the construction marks were made using a compass? A. 2 B. 3 C. 4 D What is being constructed in the figure? A. B. C. D.
3 5. An angle is a geometric figure that consists of A. two intersecting lines. B. a number between 0 and 360. C. two rays with a common endpoint. D. two distinct points and all the points between them. 6. A team of students created the following diagram based upon given information. Since the given information is unknown and is NOT listed, which is the only conclusion that can be made from the diagram created? A. B. C. D. are complementary 7. In the figure below, is parallel to Which statement proves A. If two parallel lines are cut by a transversal, the alternate interior angles are congruent. B. If two parallel lines are cut by a transversal, the alternate exterior angles are congruent. C. If two parallel lines are cut by a transversal, the corresponding angles are congruent. D. If two parallel lines are cut by a transversal, the vertical angles are congruent.
4 8. Consider this definition. A circle is the set of all points in a plane at a certain distance, its radius, from a certain point, its center. Which of the following words in the definition is an undefined term used in geometry? A. point B. radius C. center D. distance 9. In the diagram, which construction is being demonstrated? A. The first marks for constructing an altitude. B. The first marks for constructing an isosceles triangle. C. The first marks for constructing an equilateral triangle. D. The first marks for constructing a perpendicular bisector. 10. Given any three noncollinear points P, Q, and R, which geometric figure are we always able to construct? A. A circle with diameter PQ that passes through R B. A circle with center P and passing through Q and R C. A rectangle with vertices P and Q, whose diagonals intersect at R D. A triangle with vertices P, Q, and R
5 11. In this figure, lines a, b, c, d, and e intersect as shown. Based on the angle measures, which pair of lines is parallel? A. a and b B. c and e C. c and d D. d and e 12. Which of the figures below is the correct construction of an angle bisector? A. B. C. D.
6 13. Mandy was working on this proof: In these figures, What is the missing statement for the last step of Mandy s proof? A. Definition of perpendicular lines B. The transitive property of equality C. If 2 angles are congruent to equal angles, then the 2 angles are congruent. D. If 2 angles are complementary to congruent angles, then the 2 angles are congruent. 14. If and which is a valid conclusion? I II III are supplementary angles are complementary angles A. I only B. I and II C. I and III D. I, II, and III
7 15. In the figure, Lines a and b are intersected by Line t. Which of these statements proves that Lines a and b are parallel? A. B. C. D. 16. What are two lines that intersect to form right angles called? A. oblique B. parallel C. perpendicular D. skew 17. Which conjecture must be true? A. If two angles are adjacent angles, then the angles are supplementary. B. If two congruent angles are supplementary, then the angles are right angles. C. If two congruent angles have a common vertex, then the angles are vertical angles. D. If two angles are both acute angles, then the sum of the angle measures is less than 90.
8 18. In the diagram, parallel lines b and c are cut by transversal t. The informal proof below the diagram lists the reasons needed to justify 1. since vertical angles are congruent. 2. since. 3. since vertical angles are congruent. 4. due to the transitive property of equality. Which of the following is an acceptable justification for Statement 2? A. vertical angles are congruent B. corresponding angles are congruent C. remote interior angles are congruent D. alternate interior angles are congruent 19. Which statement describes two parallel lines? A. They do not intersect and they lie on the same plane. B. They do not intersect and they do not lie on the same plane. C. They intersect at a point and form right angles. D. They intersect at a point but do not form right angles.
9 20. Jordan has to prove the theorem that states: If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. She decides to solve it by indirect proof using the diagram below. Which sentence should be Jordan s first statement? A. Assume that Line r is not parallel to Line m. B. Assume are not congruent. C. Assume that Angles 1 and 2 are not consecutive. D. Assume are not supplementary.
10 21. Consider this proof: Which reason could be used to justify Statement 3 in this proof? A. subtraction property of equality B. substitution property of equality C. definition of supplementary D. definition of complementary
11 22. The piece of art below was created with strings of different lengths strung in straight line segments across the canvas. Angle 1 and Angle 2 are formed by the intersection of different strings, but both angles have a measure of 72. Which statement about the geometric relationships formed by the strings in the art must be true? A. Angle 1 and Angle 2 are complementary angles. B. Angle 1 and Angle 2 are vertical angles. C. Line t and Line n are perpendicular. D. Line s and Line t are parallel.
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Prerequisite Knowledge Conditional statement an ifthen statement (If A, then B) Converse the two parts of the conditional statement are reversed (If B, then A) Parallel lines are lines in the same plane
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12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane
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