Properties and Measurements of Parallelograms

Which statement is true for all parallelograms?

• All sides are congruent.

• Diagonals are congruent.

• Consecutive angles are supplementary.

• Diagonals are perpendicular.

In parallelogram M N P T, if the measure of angle M is (6x + 10)° and the measure of angle N is (5x + 10.5)°, what is the measure of angle T?

• 72.5°

• 83°

• 97°

• 14.5°

Which property is unique to a rhombus among parallelograms?

• Opposite sides are parallel.

• Diagonals bisect each other.

• All four sides are equal in length.

• Consecutive angles are supplementary.

In rhombus A B C D, diagonals A C and B D intersect at point E. If the perimeter of the rhombus is 60 inches and diagonal A C is 24 inches, what is the length of diagonal B D?

• 9 inches

• 12 inches

• 18 inches

• 24 inches

In a rhombus with a perimeter of 60 inches, if one diagonal measures 24 inches, what is the length of the other diagonal?

• 9 inches

• 12 inches

• 18 inches

• 24 inches

Which point of concurrency in a triangle is always equidistant from all three vertices?

• Centroid

• Incenter

• Circumcenter

• Orthocenter

In a right triangle ABC, with the right angle at B, if side AB = 15 and side BC = 20, and point F is the centroid, what is the approximate length of the segment from vertex A to the centroid F?

• 10

• 12

• 15

• 18

In triangle PMT, G is the incenter. If the length of segment GH is x + 3, and the length of segment GJ is 2x - 1, what is the measure of segment PG if PG = 4x + 1?

• 13

• 15

• 17

• 19