#1
What is the sum of interior angles of a triangle?
180 degrees
ExplanationThe sum of angles in a triangle is always 180 degrees.
#2
In a right-angled triangle, what is the relationship between the squares of the lengths of the two shorter sides and the square of the length of the hypotenuse?
The square of the hypotenuse equals the sum of the squares of the other two sides
ExplanationThis is described by the Pythagorean theorem.
#3
What is the name of a triangle with all three sides of equal length?
Equilateral triangle
ExplanationAn equilateral triangle has all sides of equal length.
#4
If two angles of a triangle are 45 degrees and 60 degrees, what is the measure of the third angle?
45 degrees
ExplanationIn a triangle, the sum of all angles is 180 degrees.
#5
What is the name of a triangle with exactly two sides of equal length?
Isosceles triangle
ExplanationAn isosceles triangle has two sides of equal length.
#6
If one angle of a triangle is 120 degrees, what is the sum of the other two angles?
60 degrees
ExplanationIn a triangle, the sum of all angles is always 180 degrees.
#7
What is the name of a triangle with all angles less than 90 degrees?
Acute triangle
ExplanationAn acute triangle has all angles less than 90 degrees.
#8
In a triangle, if one angle is greater than 90 degrees, what type of triangle is it?
Obtuse triangle
ExplanationAn obtuse triangle has one angle greater than 90 degrees.
#9
In a triangle, what is the relationship between the lengths of any two sides?
The sum of the lengths of any two sides is equal to the length of the third side
ExplanationDescribed by the triangle inequality theorem.
#10
If the lengths of the three sides of a triangle are 3, 4, and 5 units, what type of triangle is it?
Right triangle
ExplanationSatisfies the Pythagorean theorem, hence a right triangle.
#11
What is the name of the line segment joining a vertex of a triangle to the midpoint of the opposite side?
Median
ExplanationThe median of a triangle connects a vertex to the midpoint of the opposite side.
#12
What is the relationship between the areas of two similar triangles if their corresponding sides are in the ratio 2:3?
The ratio of their areas is 4:9
ExplanationArea ratio of similar triangles is the square of the corresponding side ratio.