Geometry Theorems About Triangles Test with Point Values (PDF)

Geometry math test: Theorems About Triangles – Maths PDF

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This triangle theorems test for Geometry covers theorems about triangles (Common Core G-CO.C.10), with a free PDF to print.

This 45-minute test checks triangle angle theorems, midsegments, centroids and the triangle inequality. It has 9 questions worth 20 points in total. Show every step of the work, label diagrams, and include units where they apply. Calculators are allowed unless the teacher says otherwise.

Time and points

About this test

Grade: Geometry
Chapter: Theorems About Triangles
Standards: G-CO.C.10
Time: 45 minutes
Total: 20 points

Triangle theorems test: questions

Question 1 – Angle sum [2 pts]

Triangle PQR.

The second angle of a triangle is 20° larger than the first, and the third angle is three times the first. Determine all three angles and classify the triangle by its angles.

Question 2 – Exterior angle [2 pts]

Exterior angle at B.

Find y, the exterior angle at B.

Question 3 – Apex angle [2 pts]

The apex angle of an isosceles triangle is \((6x + 4)^{\circ}\) and each base angle is \((2x + 8)^{\circ}\). Determine x and the apex angle.

Question 4 – Midsegment [3 pts]

D and E are midpoints of AB and AC.

Find the coordinates of D, the midpoint of AB, and E, the midpoint of AC. (1 point)
Find DE and BC. (1 point)
Describe how DE and BC are related. (1 point)

Question 5 – Centroid [2 pts]

A triangle has vertices (1, 2), (7, 2) and (4, 11). Find its centroid. A median from one vertex is 12 units long; how far is the centroid from that vertex?

Question 6 – Triangle inequality [3 pts]

Can sides 8, 9 and 17 form a triangle? Explain. (1 point)
Two sides measure 6 and 15. Find the range of the third side. (1 point)
Find the greatest whole-number perimeter of such a triangle. (1 point)

Question 7 – Why 180 [2 pts]

A line through vertex A of triangle ABC is parallel to BC. Explain why this shows that the angles of the triangle add to 180°.

Question 8 – Ramp angles [2 pts]

A triangular ramp support has angles in the ratio 3 : 4 : 5. Find all three angles, and decide whether it is a right triangle.

Question 9 – Equilateral side [2 pts]

An equilateral triangle has sides \(4x + 2\), \(6x – 8\) and \(3x + 7\). Find x, the side length and the measure of each angle.

Key facts behind this triangle theorems test

Key facts

Triangle angle sum: 180 degrees.
Exterior angle = sum of the two remote interior angles.
Isosceles triangle: base angles are congruent; equilateral angles are 60 degrees each.
Midsegment: parallel to the third side and half its length.
Medians meet at the centroid, two thirds of the way from each vertex.

How to use this triangle theorems test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Geometry chapters: Geometry math.

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