#1
What is the sum of the interior angles of a triangle?
180 degrees
ExplanationAngles inside a triangle add up to 180 degrees.
#2
Which theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides in a right triangle?
Pythagorean theorem
ExplanationPythagorean theorem relates the sides of a right triangle.
#3
What is the formula for the circumference of a circle?
2 × π × radius
ExplanationCircumference of a circle is 2 times π times the radius.
#4
What is the formula for calculating the area of a circle?
π × radius^2
ExplanationArea of a circle is π times the square of the radius.
#5
What is the formula for calculating the volume of a rectangular prism?
length × width × height
ExplanationVolume of a rectangular prism equals length times width times height.
#6
In a circle, what is the relationship between the radius and the diameter?
The radius is half the diameter
ExplanationRadius of a circle is half the length of its diameter.
#7
What is the formula for calculating the area of a rectangle?
length × width
ExplanationArea of a rectangle equals length multiplied by width.
#8
Which geometric concept involves a point dividing a segment into two congruent segments?
Midpoint
ExplanationMidpoint divides a segment into two equal parts.
#9
Which theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally?
Triangle proportionality theorem
ExplanationThis theorem deals with proportional division of triangle sides.
#10
What is the measure of each interior angle in a regular hexagon?
120 degrees
ExplanationEach interior angle in a regular hexagon measures 120 degrees.
#11
Which theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent?
Angle-side-angle (ASA) theorem
ExplanationThis theorem asserts congruence of triangles based on angle and side congruence.
#12
What is the measure of each exterior angle in a regular pentagon?
108 degrees
ExplanationEach exterior angle in a regular pentagon measures 108 degrees.
#13
Which theorem states that the opposite sides of a parallelogram are congruent and the opposite angles are congruent?
Parallelogram theorem
ExplanationThis theorem highlights properties of parallelograms.
#14
What is the formula for calculating the volume of a sphere?
4/3 × π × radius^3
ExplanationVolume of a sphere is calculated using this formula.
#15
What is the formula for calculating the surface area of a cylinder?
2 × π × radius × height + 2 × π × radius^2
ExplanationSurface area of a cylinder is computed using this formula.
#16
What is the formula for calculating the volume of a cone?
1/3 × π × radius^2 × height
ExplanationVolume of a cone is calculated using this formula.
#17
What is the formula for calculating the circumference of a sphere?
4 × π × radius
ExplanationCircumference of a sphere is 4 times π times the radius.
#18
Which theorem states that if a line intersects two other lines and forms congruent corresponding angles, then the two lines are parallel?
Corresponding angles postulate
ExplanationThis postulate relates to the parallelism of lines.
#19
What is the formula for calculating the surface area of a rectangular prism?
2 × (length × width + width × height + height × length)
ExplanationSurface area of a rectangular prism is computed using this formula.