Triangle Theorems Centroid Circumcenter Quiz – Geometry (10 Questions)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Standards: G-CO.C.10, G-C.A.3 · Level: Grade 10 Geometry

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What this Triangle Theorems and Triangle Centers quiz checks

• Interior angles of a triangle add to 180°; an exterior angle equals the sum of the remote interior angles.
• Base angles of an isosceles triangle are congruent, and congruent base angles mean congruent legs.
• A midsegment is parallel to the third side and half as long.
• The centroid divides each median 2 : 1; its coordinates are the averages of the vertices.
• The circumcenter is equidistant from vertices; the incenter is equidistant from sides.

The 10 questions of the quiz

1. Two angles of a triangle measure 58° and 77°. What does the third angle measure?
2. Side BC is extended past C. How large is the angle formed outside the triangle at C?
3. A base angle of an isosceles triangle measures 50°. What is the vertex angle?
4. A midsegment of a triangle is parallel to a side that is 34 units long. How long is the midsegment?
5. A median is 36 units long. How far is the centroid from the vertex?
6. Which point of a triangle is the same distance from all three vertices?
7. The circle touches all three sides of the triangle. Its center is the triangle’s:
8. What is the centroid of the triangle with vertices (1, 2), (8, 5) and (3, 11)?
9. Where is the orthocenter of a right triangle?
10. A segment joins the midpoints of two sides of a triangle. How does it relate to the third side?

After the quiz

Missed a question? Reread the Triangle Theorems and Triangle Centers lesson, then take the quiz again. Next, solve the Geometry worksheet on Triangle Theorems and Triangle Centers, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.

Mis à jour le 22 October 2026