Practice with Constructions Topic Index | Geometry Index | Regents Exam Prep Center

Answer the following questions dealing with constructions.

 1. According to the construction shown in this diagram, what would you call segment ? Choose: the bisector of angle C   the median to side the perpendicular bisector of segment   the altitude to side Explanation This construction shows a perpendicular from point C to side AB.  There is a right angle at D and CD is an altitude.

 2. This construction shows a perpendicular from a point off the line.  The reason that is perpendicular to line l  is that Choose: the locus of points equidistant from two given points is a perpendicular bisector of the segment formed by the two points. perpendicular lines always form right angles.  two congruent triangles are formed illustrating SAS. the locus of points equidistant from a given point is a circle.

 3. This diagram shows the construction of a parallel line m.  The reason that line l is parallel to line m is Choose: when two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. when two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

 4. In this construction, line segment is called the: Choose: altitude to side median to side angle bisector of angle A perpendicular to side Explanation The construction shows segment BC being bisected.  When point A is connected to point D, a median of the triangle is formed. Remember, Medians go to Midpoints.

 5. Which of the congruent triangle theorems is used in the explanation of the construction of copy an angle? Choose: SSS SAS  ASA

 6. Explain why the radius of a circle is the same length as the side of its inscribed regular hexagon. Explanation The central angle of a regular hexagon is 60º. If this central angle is 60º, the triangle formed is an equilateral triangle. Since all of the sides of an equilateral triangle are the same length, the side of the hexagon is the same length as the radius of the circle.

 7. The diagram at the left shows an inscribed regular hexagon and two inscribed triangles.  TRUE or FALSE:  The red triangle and the green triangle are equilateral triangles. Choose: true false not enough information to decide Explanation The segments joining every other vertex of the regular hexagon are equal in length, making the triangles equilateral.

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