#1
In a triangle, what is the sum of all interior angles?
180 degrees
ExplanationThe sum of all interior angles in a triangle is always 180 degrees.
#2
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
ExplanationPythagoras' theorem relates the sides of a right triangle, stating that the square of the hypotenuse equals the sum of the squares of the other two sides.
#3
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?
Isosceles triangle theorem
ExplanationThe Isosceles Triangle Theorem asserts that congruent sides in a triangle correspond to congruent angles.
#4
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
ExplanationThe Triangle Inequality Theorem stipulates that the sum of the lengths of any two sides of a triangle must exceed the length of the third side.
#5
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
ExplanationThe Sine Rule states that in a triangle, the ratio of a side length to the sine of its opposite angle is constant for all three sides.
#6
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?
Side splitter theorem
ExplanationThe Side Splitter Theorem asserts that a line parallel to one side of a triangle divides the other two sides proportionally.
#7
What is the centroid of a triangle?
The intersection point of the medians
ExplanationThe centroid of a triangle is the point where its medians intersect.
#8
What is the name of the theorem that states the perpendicular drawn from the center of a circle to a chord bisects the chord?
Intersecting chords theorem
ExplanationThe Intersecting Chords Theorem states that a perpendicular from the center of a circle to a chord bisects the chord.
#9
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
ExplanationThe Centroid Theorem asserts that the medians of a triangle intersect at a point dividing each median in a 2:1 ratio.
#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?
ASA similarity theorem
ExplanationThe ASA Similarity Theorem states that two triangles are similar if two sides and the included angle of one triangle are proportional and equal, respectively, to two sides and the included angle of another triangle.
#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?
Area proportionality theorem
ExplanationThe Area Proportionality Theorem states that the ratio of areas of similar triangles is the square of the ratio of their corresponding sides.
#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?
AAA similarity theorem
ExplanationThe AAA Similarity Theorem states that two triangles are similar if two angles of one triangle are congruent to two angles of another triangle.
#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?
Altitude-on-hypotenuse theorem
ExplanationThe Altitude-on-hypotenuse Theorem states that if an altitude is drawn from the right angle vertex of a right triangle to its hypotenuse, the resulting triangles are similar.
#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?
Mid-segment theorem
ExplanationThe Mid-segment Theorem states that a line segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
#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?
Area proportionality theorem
ExplanationThe Area Proportionality Theorem states that if two triangles are similar, the ratio of their areas equals the square of the ratio of their corresponding side lengths.