Geometry Triangle Theorems Quiz – Free PDF

Contents

This geometry triangle theorems quiz asks 10 multiple-choice questions on triangle theorems and points of concurrency, and each answer comes with a short explanation.

Ten multiple-choice questions check angle sums, exterior angles, midsegments, and the four centers of a triangle. Choose the best answer for each. The explanation after each question names the common mistake.

GeometryCommon Core: G-CO.C.10 · G-C.A.3

🎯 Triangle Theorems and Points of Concurrency – Geometry math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

The figure shows a triangle with side \(BC\) extended. What is the measure of the exterior angle at C?

Exterior angle at C.

A \(71^{\circ}\)

B \(15^{\circ}\)

C \(218^{\circ}\)

D \(109^{\circ}\)

Question 2

Two angles of a triangle measure \(74^{\circ}\) and \(38^{\circ}\). What is the third angle?

A \(112^{\circ}\)

B \(68^{\circ}\)

C \(106^{\circ}\)

D \(142^{\circ}\)

Question 3

What is the measure of each base angle of this isosceles triangle?

Isosceles triangle.

A \(52^{\circ}\)

B \(76^{\circ}\)

C \(64^{\circ}\)

D \(128^{\circ}\)

Question 4

D and E are midpoints of \(\overline{AB}\) and \(\overline{AC}\), and \(BC=34\). What is \(DE\)?

Midsegment DE.

A 68

B 34

C 51

D 17

Question 5

G is the centroid of a triangle and the median from vertex A has length 24. How far is G from A?

A 12

B 8

C 16

D 18

Question 6

Which point of concurrency is the same distance from all three vertices of a triangle?

A circumcenter

B incenter

C centroid

D orthocenter

Question 7

Which point of concurrency is found where the three altitudes of a triangle meet?

A circumcenter

B orthocenter

C incenter

D centroid

Question 8

A circle touches all three sides of a triangle from the inside. Its center is where which lines meet?

Inscribed circle.

A the perpendicular bisectors

B the medians

C the angle bisectors

D the altitudes

Question 9

A triangle has vertices \((0,0)\), \((6,0)\), and \((3,9)\). What are the coordinates of its centroid?

A \((3,4.5)\)

B \((3,6)\)

C \((4.5,3)\)

D \((3,3)\)

Question 10

A right triangle has legs of 6 and 8. What is the radius of its circumscribed circle?

A \(5\text{ units}\)

B \(10\text{ units}\)

C \(4\text{ units}\)

D \(7\text{ units}\)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Interior angles sum to 180 degrees; an exterior angle equals the sum of the two remote interior angles.
Base angles of an isosceles triangle are congruent, and the converse is true.
A midsegment is parallel to the third side and half its length.
Medians meet at the centroid, two thirds of the way from each vertex.
The circumcenter is the center of the circumscribed circle; the incenter is the center of the inscribed circle.