PROPERTIES OF PARALLELOGRAM WORKSHEET

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Problem 1 :

Find each measure in parallelogram

Find,

1) ML 2) LP 3) ∠LPM 4) ∠MLN 5) LN 6) QN

Solution

Problem 2 :

CDEF is a parallelogram. Find each measure.

(i) CD (ii) EF (iii) ∠E (iv) ∠F

Solution

Problem 3 :

Quadrilateral RSTU is a parallelogram. Find the values of x, y, a, and b.

Solution

Problem 4 :

Solution

Problem 5 :

Find the missing measurements of parallelogram.

Find the measures of

1) CD

2) AC

3) CE

4) DA

5) DB

6) DE

7) ∠ABC

8) ∠BCD

9) ∠BAD

10) ∠DAE

11) ∠BCD

12) ∠BCE

13) ∠ADC

14) ∠CDE

15) ∠EAB

16) ∠CED

17) ∠EDA

18) ∠AEB

19) ∠DEA

Solution

Problem 6 :

In the figure given below, ABCD is a parallelogram. Find the values of x, y, z and p.

Solution

Problem 7 :

State whether each statement is always, sometimes, or never true for a parallelogram. Explain your reasoning.

a. The opposite sides are congruent.

b. All four sides are congruent.

c. The diagonals are congruent.

d. The opposite angles are congruent.

e. The adjacent angles are congruent.

f. The adjacent angles are complementary

Solution

Answer Key

1) ML = 12 m,

2) LP = 10 m

3) ∠LPM = 62°

4) ∠MLN = 32°

5) LN = 18

6) QN = 9 m

2) (i) CD = 36 (ii) EF = 36 (iii) ∠E = 132 (iv) ∠F = 48

3) x = 80°, y = 100, a = 6 and b = 9

4) x = 100, y = 45 and b = 9

1) CD = 10

2) AC = 26

3) CE = 13

4) DA = 22

5) DB = 24

6) DE = 12

7) ∠ABC = 110

8) ∠BCD = 70

9) ∠BAD = 70

10) ∠DAE = 23

11) ∠BEC = 119

12) ∠BCE = 23

13) ∠ADC = 110

14) ∠CDE = 72

15) ∠EAB = 47

16) ∠CED = 61

17) ∠EDA = 38

18) ∠AEB = 61

19) ∠DEA = 119

6) x = 110 and p = 70

a. In parallelogram, always opposite sides will be congruent.

b. In parallelogram, sometimes all four sides will be congruent. Then it is rhombus.

c. In parallelogram, sometimes the diagonals are congruent.

d. The opposite angles are congruent always.

e. Sometimes the adjacent angles are congruent. When adjacent angles are equal, its measure must be 90 degree, then that shape is known as rectangle.

f. The adjacent angles will never be complementary, because the sum of adjacent angles must be add up to 180 degree.

Problem 1 :

For the parallelogram given below, solve for m and n.

Solution

Problem 2 :

For the parallelogram given below, solve for j and k.

Solution

Problem 3 :

In parallelogram PQRS, solve for x and y.

Solution

Problem 4 :

Solve the n in the following parallelogram ABCD. Find length of the diagonal BD.

Solution

Problem 5 :

Length of the longer diagonal in the parallelogram FAST.

Solution

Problem 6 :

For what value of x is quadrilateral MNPQ a parallelogram? Explain your reasoning

Solution

Problem 7 :

find the value of x that makes the quadrilateral a parallelogram.

Solution

Problem 8 :

Solution

Problem 9 :

What value of x makes the quadrilateral a parallelogram? Explain how you found your answer.

Solution

Problem 10 :

Find the value of each variable in the parallelogram.

Solution

Problem 11 :

Find the coordinates of the intersection of the diagonals of ▱QRST with vertices Q(−8, 1), R(2, 1), S(4, −3), and T(−6, −3).

Solution

Problem 12 :

As shown in the diagram below, the diagonals of parallelogram QRST intersect at E. If QE = x²+ 6x, SE = x + 14, and TE = 6x − 1, determine TE algebraically

Solution

Answer Key

1) m = 4, n = 5

2) k = 2 and j = 4.5

3) x = 5 and y = 6

4) n = 58, length of the diagonal BD is 336.

5) length of the longer diagonal is 46.

6) the value of x is 2.

7) the value of x is 8

8) the value of x is 2/3.

9) x = 5

10) c = 6 and d = 10

11) (-2, -1)

12) the length TE is 11.

Problem 1 :

From the parallelogram given below, find the value of x, y and z.

Solution

Problem 2 :

If one angle of a parallelogram is 24 degree less than twice the smallest angle then, find the largest angle of the parallelogram.

Solution

Problem 3 :

In a parallelogram PQRS, if

∠P = (3x − 5)° and ∠Q = (2x + 15)°

then find the value of x.

Solution

Problem 4 :

If PQRS is a parallelogram, then ∠P − ∠R is

(a) 90° (b) 45° (c) 60° (d) 0°

Solution

Problem 5 :

Two adjacent angles of a parallelogram are 3x - 4 and 3x + 10. Find the angles of parallelogram.

Solution

Problem 6 :

One angle of a parallelogram is 60 degree. Find its opposite angle and the adjacent angle.

Solution

Problem 7 :

Find the indicated measure in parallelogram MNOP, explain your reasoning.

a) PO

b) QO

c) NO

d) PQ

e) m∠PMN

f) m∠NOP

g) m∠OPM

h) m∠NMO

Solution

Problem 8 :

Solution

Problem 9 :

Solution

Problem 10 :

Find the value(s) of the variable(s) in each parallelogram

Solution

Problem 11 :

Two consecutive angles in a parallelogram have measures x + 5 and 4x - 10. Find the measure of the smaller angle.

Solution

Answer Key

1) x = 40, y = 40 and z = 40

2) the largest angle measure is 112.

3) x = 34

4) ∠P − ∠R = 0

5) the angles are 83 and 97.

6) In parallelogram, opposite angle will be equal. Opposite angle 60 degree is also 60 degree.

7) a) PO = 24 units

b) OQ = 14 units

c) NO = 26 units

d) PQ = 20.7 units

e) m∠PMN = 112

f) m∠NOM = 53

g) m∠OPM = 68

h) m∠NMO = 59 (Alternate interior angles are equal)

8) u = 66 and v = 38

9) a = 7 and b = 41

10) the value of a is 20.

11) the smaller angle measure is 32 degree.

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PROPERTIES OF PARALLELOGRAM WORKSHEET

Answer Key

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Answer Key

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