Congruent Angle Constructions — Practice Geometry Questions

By Allen Ma, Amber Kuang

You can use your knowledge of geometric constructions (as well as a compass and straight edge) to create congruent angles. The following practice questions test your construction skills.

If you’re drawing two arcs for a construction, make sure you keep the width of the compass (or radii of the circles) consistent.

Practice questions

image0.png

  1. Use the above figure to construct

    image1.png

    an angle congruent to angle A.

    image2.png

  2. Use the above figure to construct

    image3.png

    a triangle congruent to triangle BCA.

Answers and explanations

  1. 1.Here is the solution:

    image4.png

    Use a straight edge to draw a ray with endpoint D. Place the compass point on A, and with any width, draw an arc intersecting the angle at two points.

    image5.png

    Using the same width, place the compass point at D and make an arc.

    image6.png

    Using the compass, measure the distance between B and C. Keeping that compass width, place the compass point at E and draw an arc. Connect the point where the arcs intersect to D.

    image7.png

  2. 2.Here is the solution:

    image8.png

    Place the compass point at B and measure the length of

    image9.png

    Draw Point D on your paper. Keeping the length of

    image10.png

    place the compass point on D and draw an arc. Place a point on the arc and label it E.

    image11.png

    Use your compass to measure the length of

    image12.png

    Keeping that compass width, place the compass point at D and draw an arc where the third vertex would be located.

    image13.png

    Use your compass to measure the length of

    image14.png

    Keeping that compass width, place the compass point at E and draw an arc where the third vertex would be. Name the point where the arcs intersect F. Connect the three vertices of the triangle.

    image15.png