Geometric Properties and Theorems of Triangles Quiz

Test your knowledge of triangle geometry with this quiz. Explore the sum of angles, theorems about sides and angles, centroids, and more.

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In a triangle, what is the sum of all interior angles?

90 degrees

180 degrees

270 degrees

360 degrees

What is the name of the theorem that states the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides?

Pythagoras' theorem

Euclid's theorem

Fermat's theorem

Euler's theorem

What is the name of the theorem that states if two sides of a triangle are congruent, then the angles opposite those sides are also congruent?

Angle bisector theorem

Pythagoras' theorem

Isosceles triangle theorem

Mid-segment theorem

What is the name of the theorem that states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side?

Triangle inequality theorem

Similar triangles theorem

Heron's theorem

Euler's theorem

What is the name of the theorem that states the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides of the triangle?

Sine rule

Cosine rule

Tangent rule

Ceva's theorem

What is the name of the theorem that states if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally?

Angle bisector theorem

Mid-segment theorem

Side splitter theorem

Thales' theorem

What is the centroid of a triangle?

The intersection point of the medians

The intersection point of the altitudes

The intersection point of the perpendicular bisectors

The intersection point of the angle bisectors

What is the name of the theorem that states the perpendicular drawn from the center of a circle to a chord bisects the chord?

Power of a point theorem

Intersecting chords theorem

Inscribed angle theorem

Thales' theorem

What is the name of the theorem that states the medians of a triangle intersect at a point that divides each median into segments in the ratio 2:1?

Centroid theorem

Mid-segment theorem

Apollonius' theorem

Median theorem

#10

What is the name of the theorem that states if two sides of one triangle are proportional to two sides of another triangle, and their included angles are equal, then the two triangles are similar?

SAS similarity theorem

AAA similarity theorem

SSS similarity theorem

ASA similarity theorem

#11

What is the name of the theorem that states the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides?

Similarity theorem

Area proportionality theorem

Triangle proportionality theorem

Pythagorean theorem

#12

What is the name of the theorem that states if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar?

Angle-angle similarity theorem

SSS similarity theorem

SAS similarity theorem

AAA similarity theorem

#13

What is the name of the theorem that states if the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two triangles formed are similar to the original triangle and to each other?

Median theorem

Apollonius' theorem

Altitude-on-hypotenuse theorem

Inscribed angle theorem

#14

What is the name of the theorem that states if a line segment connects the midpoints of two sides of a triangle, then it's parallel to the third side, and its length is half the length of the third side?

Midpoint theorem

Mid-segment theorem

Angle bisector theorem

Similarity theorem

#15

What is the name of the theorem that states if two triangles are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths?

Altitude-on-hypotenuse theorem

Apollonius' theorem

Angle bisector theorem

Area proportionality theorem

Geometric Properties and Theorems of Triangles Quiz

In a triangle, what is the sum of all interior angles?

What is the name of the theorem that states the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides?

What is the name of the theorem that states if two sides of a triangle are congruent, then the angles opposite those sides are also congruent?

What is the name of the theorem that states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side?

What is the name of the theorem that states the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides of the triangle?

What is the name of the theorem that states if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally?

What is the centroid of a triangle?

What is the name of the theorem that states the perpendicular drawn from the center of a circle to a chord bisects the chord?

What is the name of the theorem that states the medians of a triangle intersect at a point that divides each median into segments in the ratio 2:1?

What is the name of the theorem that states if two sides of one triangle are proportional to two sides of another triangle, and their included angles are equal, then the two triangles are similar?

What is the name of the theorem that states the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides?

What is the name of the theorem that states if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar?

What is the name of the theorem that states if the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two triangles formed are similar to the original triangle and to each other?

What is the name of the theorem that states if a line segment connects the midpoints of two sides of a triangle, then it's parallel to the third side, and its length is half the length of the third side?

What is the name of the theorem that states if two triangles are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths?

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