Understanding Quadrilaterals

Exercise 3

1. Given a parallelogram ABCD. Complete each statement along with the definition or property used.

2. Consider the following parallelograms. Find the values of the unknowns x, y, z.

(i)

(ii)

Answer: x, y and z will be complementary to 50°.

So, Required angle = 180° - 50° = 130°

(iii)

Answer: z being opposite angle= 80°

x and y are complementary, x and y

= 180° - 80° = 100°

(iv)

Answer: As angles on one side of a line are always complementary

So, x = 90°

So, y = 180° - (90° + 30°) = 60°

The top vertex angle of the above figure = 60° x 2=120°

Hence, bottom vertex Angle = 120° and

z = 60°

(v)

Answer: y= 112°, as opposite angles are equal in a parallelogram

x= 180°-(112°-40°)=28°

As adjacent angles are complementary so angle of the bottom left vertex

=180°-112°=68°

So, z=68°-40°=28°

Another way of solving this is as follows:

As angles x and z are alternate angles of a transversal so they are equal in measurement.

3. Can a quadrilateral ABCD be a parallelogram if

Answer: (i)It can be , but not always as you need to look for other criteria as well.

(ii) In a parallelogram opposite sides are always equal, here AD BC, so its not a parallelogram.

(iii) Here opposite angles are not equal, so it is not a parallelogram.

5. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.

Answer: Opposite angles of a parallelogram are always add upto 180°.

6. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Answer: 90°, as they add up to 180°

7. The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

Answer: Angle opposite to y = 180° - 70°=110°

Hence, y = 110°

x = 180° - (110° + 40°) = 30°, (triangle’s angle sum)

z = 30° (Alternate angle of a transversal)

8. The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)

Answer: As opposite sides are equal in a parallelogram

Answer: As you know diagonals bisect each other in a parallelogram.

9. In the given figure both RISK and CLUE are parallelograms. Find the value of x.

Answer: In parallelogram RISK