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Chapter: Quadrilaterals Section: Exercises

Problem: 1

Make a concept map (a tree diagram or a Venn diagram) to organize these quadrilaterals: rhombus, rectangle, square, trapezoid.


Problem: 2

Draw and label the following:

Rhombus EQUL with diagonals EU and QL intersecting at A .


Problem: 3

What type (or types) of quadrilateral has only rotational symmetry?


Problem: 4

Consider the parallelogram shown alongside. Complete the statement given below, giving reasons.

Δ OAD is congruent to?


Problem: 5

Draw a pair of parallel lines by tracing along both edges of your ruler. Draw a transversal. Use your compass to bisect each angle of a pair of alternate interior angles. What shape is formed? Can you explain why?


Problem: 6

Parallelogram ABCD is shown in the figure. Find the values of a , b , x , and y .


Problem: 7

The figure shown is a parallelogram. Obtain the values of a , b , and c .


Problem: 8

The figure shown consists of two parallelograms, WXYZ and ABCD . Find the measure of angle WAD .


Problem: 9

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram .

Sketch and label a diagram. List what is given and what is to be proved. Then write a two–column proof of the above statement.


Problem: 10

Consider rectangle JKLM shown in the figure.

If JL = 6 y – 21 and MN = 2 y + 9, find y .


Problem: 11

If the quadrilateral shown is a parallelogram, what must be the values of a and b ?


Problem: 12

Find the perimeter of quad. LNOK if L , M , and N are the midpoints of the sides of Δ TKO in the given figure.


Problem: 13

The angles of a quadrilateral measure 2 x , x + 30, x + 50, and 2 x – 20. The quadrilateral could be:

(a) square (b) parallelogram (c) trapezoid

I. (a) or (b)

II. (b) or (c)

III. (a) alone

IV. (b) alone

V. (c) alone


Problem: 14

Quadrilateral PQRS has vertices P (–2, 2), Q (5, 9), R (8, 6), and S (1, –1). Is PQRS a rectangle? Determine using slopes.


Problem: 15

Consider rectangle JKLM shown in the figure. If m 5 = 15, find m 3.


Problem: 16

Using straightedge and compass, construct an isosceles trapezoid PQRS with legs of length y units.


Problem: 17

In kite ABCD , AB = 13, BC = 6, and BD = 10. Find AE , EC , and AC .


Problem: 18

Consider rhombus JKLM shown in the figure. Find m JLK , given that m JKL is 145.


Problem: 19

The vertices of quadrilateral ABCD are

A = (–2, –4), B = (2, –7), C = (6, –4), and D = (2, –1). Determine whether ABCD is a square, a rhombus, a rectangle, or a parallelogram. List all names that apply.


Problem: 20

PQRS is a rhombus. Find RS and the coordinates of the midpoint of .


Problem: 21

In the figure, and are the bases of trapezoid ABCD . Find the coordinates of median for ABCD . Show that || .


Problem: 22

In the figure shown, and are the bases of trapezoid PQRS and . Prove that PQRT is a parallelogram.


Problem: 23

A , B , C , and D are the midpoints of the sides of isosceles trapezoid PQRS . What type of quadrilateral is ABCD ?


Problem: 24

Verify whether the polygons satisfy the given property. If yes, then put check marks in the appropriate spaces in the table.


Problem: 25

Draw a rectangle. Join the midpoints of the sides in order.

Identify the special kind of quadrilateral you appear to get.