Geometry Proofs

Prove that the opposite sides of a parallelogram are equal.

• Opposite sides of a parallelogram are equal because they are parallel and congruent.

• Opposite sides of a parallelogram are equal because they are intersecting and congruent.

• Opposite sides of a parallelogram are equal because they are perpendicular and congruent.

• Opposite sides of a parallelogram are equal because they are adjacent and congruent.

If angle A = 60 degrees, find the value of angle B in a triangle where angle C = 90 degrees.

• 30 degrees

• 120 degrees

• 75 degrees

• 45 degrees

Fill in the blank: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the _________.

• median

• perimeter

• angles

• legs

State the property that justifies the statement: 'If two angles are complementary to the same angle, then they are congruent.'

• Vertical angles are congruent.

• Adjacent angles are congruent.

• Supplementary angles are congruent.

• Corresponding angles are congruent.

Explain why the sum of the interior angles of a triangle is always 180 degrees.

• The sum of the interior angles of a triangle is always 180 degrees.

• The sum of the interior angles of a triangle is 270 degrees.

• The sum of the interior angles of a triangle is 360 degrees.

• The sum of the interior angles of a triangle is 90 degrees.

If a quadrilateral has one pair of opposite sides parallel and equal, what type of quadrilateral is it?

• Trapezoid

• Parallelogram

• Rhombus

• Rectangle

In a circle, if a central angle is 90 degrees, what is the measure of the corresponding inscribed angle?

• 60 degrees

• 75 degrees

• 30 degrees

• 45 degrees

True or False: The diagonals of a rectangle are always equal in length.

• Depends on the rectangle

• Sometimes

• False

• True

Given a rectangle with a length of 8 cm and a width of 6 cm, calculate the perimeter of the rectangle.

• 20 cm

• 24 cm

• 28 cm

• 32 cm