Geometric Constructions
Math ⇒ Geometry
Geometric Constructions starts at 6 and continues till grade 12.
QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Geometric Constructions.
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See sample questions for grade 12
Describe the steps to construct a 60° angle at a given point on a line using only a compass and straightedge.
Describe the steps to construct a parallel line to a given line through a point not on the line using only a compass and straightedge.
Describe the steps to construct the geometric mean of two given segments.
Describe the steps to construct the perpendicular bisector of a given line segment using only a compass and straightedge.
Explain how to construct a tangent to a circle from a point outside the circle.
Given a segment AB, construct a square with AB as one of its sides. Describe the steps.
Given a segment AB, construct a square with AB as one of its sides. Describe the steps.
Given a triangle with vertices A, B, and C, describe how to construct the circumcircle.
Which construction is used to find the center of a given circle? (1) Drawing two chords and their perpendicular bisectors (2) Drawing a tangent (3) Drawing a diameter (4) Drawing a secant
Which of the following constructions can be used to divide a given segment into n equal parts? (1) Drawing n circles (2) Using a protractor (3) Drawing a ray at an angle and marking n equal segments (4) Drawing perpendicular bisectors repeatedly
Which of the following constructions is impossible using only a compass and straightedge? (1) Constructing a perpendicular bisector (2) Doubling the cube (3) Bisecting an angle (4) Drawing a parallel line through a point
Which of the following is a necessary step in constructing the angle bisector of a given angle? (1) Drawing a perpendicular bisector (2) Drawing arcs from the vertex and intersection points (3) Drawing a tangent (4) Drawing a median
Fill in the blank: The ______ is the point of intersection of the altitudes of a triangle.
Fill in the blank: The ______ is the point of intersection of the perpendicular bisectors of a triangle.
Fill in the blank: The ______ of a triangle is the point of intersection of its altitudes.
Fill in the blank: The ______ of a triangle is the point of intersection of its medians.
Is it possible to trisect any arbitrary angle using only a compass and straightedge?
True or False: A perpendicular bisector of a segment always passes through the midpoint of the segment.
True or False: The angle bisectors of a triangle are always concurrent.
True or False: The center of a circle can be constructed by drawing two non-parallel chords and their perpendicular bisectors.
