Regents Exam Questions by Topic Page 1 TOOLS OF GEOMETRY: Constructions NAME:

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1 Regents Exam Questions by Topic Page ge, P.I. G.G.17 Which illustration shows the correct construction of an angle bisector? [A] a, P.I. G.G.17 Using only a ruler and compass, construct the bisector of angle BAC in the accompanying diagram. [B] [C] [D] 4. fall0804ge, P.I. G.G.18 The diagram below shows the construction of the perpendicular bisector of AB. 2. fall0832ge, P.I. G.G.17 the bisector of the angle shown below. [Leave all construction marks.] Which statement is not true? [A] AC CB [B] CB 1 AB 2 [C] AC 2 AB [D] AC CB AB

2 Regents Exam Questions by Topic Page a, P.I. G.G.18 the perpendicular bisector of AB shown below. Show all construction marks a, P.I. G.G.19 In the accompanying diagram of a construction, what does PC represent? [A] an altitude drawn to AB a, P.I. G.G.18 Using only a compass and a straightedge, construct the perpendicular bisector of AB and label it c. [Leave all construction marks.] [B] the perpendicular bisector of AB [C] the bisector of APB [D] a median drawn to AB a, P.I. G.G.19 the line that is perpendicular to AB and that passes through point P. Show all construction marks.

3 Regents Exam Questions by Topic Page ge, P.I. G.G.19 a line that passes through point P and is perpendicular to line m. [Leave all construction marks.] a On the accompanying diagram of ABC, use a compass and a straightedge to construct a median from A to BC a Construct a triangle with sides of lengths a, b, and c, as shown below. Be sure the longest side of your triangle lies on PQ and that point P is one of the triangle's vertices. [Show all arcs necessary for a valid construction.] 10. fall0807ge, P.I. G.G.19 The diagram below illustrates the construction of PS parallel to RQ through point P. Which statement justifies this construction? [A] m 1 m 2 [B] m 1 m 3 [C] PR RQ [D] PS RQ

4 Regents Exam Questions by Topic Page 1 [1] C [2] [3] [4] C [5] [2] A correct construction is drawn showing all appropriate arcs, and the angle bisector is drawn. [1] All construction arcs are drawn, but the angle bisector is not drawn. or [1] The appropriate method is demonstrated, but one construction error is made, such as not extending the sides to show points of intersection by the arc. [2] A correct construction is drawn to find the midpoint of BC, showing both sets of arcs and a line connecting A with the midpoint. [1] A correct construction is drawn to find the midpoint of BC, but the median is not drawn. or [1] The construction is appropriate, but a compass and a straightedge are not used. [0] No construction arcs are shown. the arcs intersecting above and below AB, and the perpendicular line is drawn. [1] All of the construction arcs are drawn, but the perpendicular line is not drawn. [6] [7] A [8] [9] [10] A the arcs intersecting above and below AB, and line c is drawn. [1] A correct construction is drawn, but line c is not labeled. [0] A drawing that is not a construction is shown with arc marks sketched. all necessary arcs. [1] All of the construction arcs are drawn, but the perpendicular line is not drawn. or [1] A line perpendicular to AB is constructed correctly, but it does not pass through point P. [2] A correct construction is drawn showing all appropriate arcs, and the perpendicular line is drawn. [1] Appropriate work is shown, but one construction error is made, such as not drawing the perpendicular line. or [1] Appropriate work is shown, but one conceptual error is made.

5 Regents Exam Questions by Topic Page 2 [11] [12] [2] A correct construction is drawn to find the midpoint of BC, showing both sets of arcs and a line connecting A with the midpoint. [1] A correct construction is drawn to find the midpoint of BC, but the median is not drawn. or [1] The construction is appropriate, but a compass and a straightedge are not used. [0] No construction arcs are shown. [2] A correct triangle with the longest side on PQ and a vertex at P is drawn, and three appropriate arcs are shown. [1] A correct triangle is constructed on PQ, but P is not a vertex. or [1] A correct triangle is constructed with no sides on PQ. [0] A triangle that is not congruent to the correct solution or a triangle with less than three arcs is shown.