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 11
Describe how to construct a triangle given two angles and the included side (ASA construction).
Describe the steps to construct a 60° angle using only a compass and straightedge.
Describe the steps to construct a triangle given its three sides (SSS construction).
Explain why it is impossible to construct a triangle with sides 2 cm, 3 cm, and 6 cm.
Given a circle with center O and a point P outside the circle, explain how to construct the tangents from P to the circle.
Given a triangle with sides 5 cm, 7 cm, and 8 cm, describe how you would construct it using only a ruler and compass.
If you are given a line segment AB, how do you construct its perpendicular bisector?
To construct a regular hexagon inscribed in a circle, what is the relationship between the radius of the circle and the side of the hexagon?
A triangle has vertices at A(0,0), B(6,0), and C(2,4). Calculate the coordinates of the centroid of the triangle.
Describe the steps to construct a triangle given the base, the base angle at one end, and the sum of the other two sides.
Explain how to construct a triangle given two sides and a non-included angle (SSA construction), and discuss under what conditions this construction yields zero, one, or two possible triangles.
Given a circle with center O and a chord AB, describe how to construct the midpoint of the arc AB that does not contain a given point C on the circle.
Given a triangle ABC, describe the steps to construct the excenter opposite vertex A using only a compass and straightedge.
