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Geometry Exercises: Parallelograms, Rhombuses, Kites, and Trapezoids, Exams of Mathematics

Chamberlain College of NursingMathematics

A collection of geometry exercises focused on quadrilaterals, specifically parallelograms, rhombuses, kites, and trapezoids. It includes various problems that test understanding of properties, theorems, and relationships related to these shapes. The exercises are designed to reinforce key concepts and provide practice in applying geometric principles to solve problems.

Typology: Exams

2024/2025

Available from 03/14/2025

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Math; Questions With All Correct
Answer
Given: Parallelogram HIJK with diagonals intersecting at L
Prove: / Correct answer-2) Opposite sides in a parallelogram are congruent
3) Diagonals of a parallelogram bisect each other
4) SSS
5) CPCTC
The diagonals of parallelogram DEFG intersect at H. What congruence statements can you make about
the parallelogram? Correct answer-HE = HG, HD = HF, ED = FG, EF = DG, angle GDE = angle EFG, and
angle DEF = FGD. There are countless others, such as certain angles totaling 180 degrees.
Explain how certain values of x and y make ABCD a parallelogram. Correct answer-In order for ABCD
to be a parallelogram, the diagonals must bisect each other. If segment AC bisects segment BD, then 4y -
5 = 2y + 1. Solving this equation, we get that y = 3. If segment BD bisects segment AC, then 4x = x + 3, so
x = 1. Therefore, if x = 1 and y = 3, then ABCD is a parallelogram.
Quadrilateral ABCD has side lengths of AB = 13w - 5, BC = 5z - 2, CD = 13w - 5, and AD = 3z + 5. Find the
value of z for which quadrilateral ABCD is a parallelogram. Correct answer-7/2
In quadrilateral HELP, /. What other condition would prove that HELP is a parallelogram? Correct
answer-HE = LP
Describe a method for verifying that quadrilateral EFGH is a parallelogram if only the interior angle
measures of EFGH are known. Explain your answer. Correct answer-By the converse of the
parallelogram angle theorem, if both pairs of opposite angles are congruent, then quadrilateral EFGH is
a parallelogram.
Which of the following is not always true? Correct answer-In a rhombus, the diagonals are
perpendicular.
The diagonals of rhombus WXYZ intersect at point P. If WP = 4 and ZP = 3, find the perimeter of the
rhom Correct answer-20.
ABCD is an isosceles trapezoid. If AD = BC, B= x+10 and C= 2x-30, find the measure of angle D Correct
answer-130 degrees.
Which statement about kite PQRS must be true? Correct answer-RP is perpendicular to QS.
Given: Isosceles trapezoid ABCD with AB=CD
Prove: A and C are supplementary. Correct answer-Statement : Reason
1. Isosceles trapezoid ABCD : Given
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Math; Questions With All Correct

Answer

Given: Parallelogram HIJK with diagonals intersecting at L Prove: / Correct answer-2) Opposite sides in a parallelogram are congruent

  1. Diagonals of a parallelogram bisect each other
  2. SSS
  3. CPCTC The diagonals of parallelogram DEFG intersect at H. What congruence statements can you make about the parallelogram? Correct answer-HE = HG, HD = HF, ED = FG, EF = DG, angle GDE = angle EFG, and angle DEF = FGD. There are countless others, such as certain angles totaling 180 degrees. Explain how certain values of x and y make ABCD a parallelogram. Correct answer-In order for ABCD to be a parallelogram, the diagonals must bisect each other. If segment AC bisects segment BD, then 4y - 5 = 2y + 1. Solving this equation, we get that y = 3. If segment BD bisects segment AC, then 4x = x + 3, so x = 1. Therefore, if x = 1 and y = 3, then ABCD is a parallelogram. Quadrilateral ABCD has side lengths of AB = 13w - 5, BC = 5z - 2, CD = 13w - 5, and AD = 3z + 5. Find the value of z for which quadrilateral ABCD is a parallelogram. Correct answer-7/ In quadrilateral HELP, /. What other condition would prove that HELP is a parallelogram? Correct answer-HE = LP Describe a method for verifying that quadrilateral EFGH is a parallelogram if only the interior angle measures of EFGH are known. Explain your answer. Correct answer-By the converse of the parallelogram angle theorem, if both pairs of opposite angles are congruent, then quadrilateral EFGH is a parallelogram. Which of the following is not always true? Correct answer-In a rhombus, the diagonals are perpendicular. The diagonals of rhombus WXYZ intersect at point P. If WP = 4 and ZP = 3, find the perimeter of the rhom Correct answer-20. ABCD is an isosceles trapezoid. If AD = BC, B= x+10 and C= 2x-30, find the measure of angle D Correct answer-130 degrees. Which statement about kite PQRS must be true? Correct answer-RP is perpendicular to QS. Given: Isosceles trapezoid ABCD with AB=CD Prove: A and C are supplementary. Correct answer-Statement : Reason
  1. Isosceles trapezoid ABCD : Given
  1. Segment AB is parallel to segment CD : Given
  2. Angle A is supplementary to angle D : Consecutive interior angles of parallel lines are supplementary
  3. Measure of angle A + measure of angle D = 180 degrees : Definition of supplementary
  4. Angle D is congruent to angle C : Base angles of an isosceles trapezoid are congruent
  5. Measure of angle A + measure of angle C = 180 degrees : Substitution
  6. Angle A and angle C are supplementary : Definition of supplementary ABCD is an isosceles trapezoid. If AC= BC, angle B= 60, and angle C= 3x+15, find the measure of angle A Correct answer-120 degrees. The diagonals of kite KITE intersect at point P. If TKE= x+6 and IEK= 2x, find IKE Correct answer-68. Quadrilateral ABCD is an isosceles trapezoid with AC=BC The base angles are Correct answer-D. A and D as well as B and C. A kite is a Correct answer-quadrilateral. ABCD is an isosclese trapezoid with AD || BC, B= 60, C = (3x +15) Solve for x Correct answer-15. AB|| CD, AC = 7y-30, BD= 4y + 60, CD= 5y +14, Find the length of CD. Correct answer-164. ^ Solve for Y. Correct answer- The diagonals of kite PQRS intersect at point T. Which statement is not true? Correct answer-QRS = QPS AB= m + 6, CD = 3m +2, BC = 3m, AD= 7m-16. Solve for M Correct answer- Find the values of W and X that make NOPQ a parallelogram. ( w+7, 5w-5), (3/2x, 3) Correct answer-D. w= 3, x = 1/ The diagonals of parallelogram ABCD intersect at point E. To prove that ADE=CBE, all of the following could be used, except for which. Correct answer-D. ACD=CAB by SSS. Quadrilateral ABCD is a parallelogram, AC bisects DAB and BCD, BD bisects ABC and CDA, AC bisects BD, AC is perpendicular to BD, and the diagonals are not congruent. What is the best name for quad. ABCD? Correct answer-Rhombus. The diagonals of kite intersect at point P. if KIP=46, and KEP=34. Find ITE. Correct answer-D. 100. Which statement is true? Correct answer-C. An isosceles trapezoid has perpendicular diagonals.