Triangle Theorems and Points of Concurrency: Geometry Math Quiz – PDF Download
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
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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.
A68
B34
C51
D17
Question 5
G is the centroid of a triangle and the median from vertex A has length 24. How far is G from A?
A12
B8
C16
D18
Question 6
Which point of concurrency is the same distance from all three vertices of a triangle?
Acircumcenter
Bincenter
Ccentroid
Dorthocenter
Question 7
Which point of concurrency is found where the three altitudes of a triangle meet?
Acircumcenter
Borthocenter
Cincenter
Dcentroid
Question 8
A circle touches all three sides of a triangle from the inside. Its center is where which lines meet? Inscribed circle.
Athe perpendicular bisectors
Bthe medians
Cthe angle bisectors
Dthe 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!
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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.
