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QUESTION: 1

Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?

Solution:

A **quadrilateral is** a rhombus if: it **is** a parallelogram, and a **pair of adjacent sides** are **equal**, its **diagonals** bisect each other at **right angles**, its **diagonals** bisect each vertex **angle.**

QUESTION: 2

If the sides of a triangle are produced in order, Prove that the sum of the exterior angles so formed is 360°.

Solution:

Suppose you have a ∆ABC

All the exterior angles will be equal to

(180-A)°

(180-B)°

(180-C)°

respectively (Angles on the same line) so if you sum it up it will be equal to 540 - (A+ B + C )

And by angle sum property A+B+C = 180°

Therefore Sum = 540 - 180 = 360°

QUESTION: 3

Given a parallelogram ABCD. AD = ....

Solution:
BC ( because of opposite sides of the parallelogram are equal = )

QUESTION: 4

The sum of the measures of the three angles of a triangle is ______.

Solution:

Angle sum property of a triangle is that sum of 3 angles is 180º

QUESTION: 5

The ________ of a rhombus are perpendicular bisectors of one another.

Solution:

QUESTION: 6

Find the value of the unknown x in this parallelogram.

Solution:

QUESTION: 7

The opposite sides of a parallelogram are of ________ length.

Solution:

It’s a property of parallelogram that opposite sides of a parallelogram are equal and parallel.

QUESTION: 8

Which of the parallelograms has all sides equal and diagonals bisect each other at right angle?

Solution:

The **diagonals of a parallelogram** only **bisect each other at right angles** if the **parallelogram is** a rhombus.

QUESTION: 9

Solution:

Sum of the exterior angles of regular polygon = 360degree

But each exterior angle = 45degree

number of sides of regular polygon = 360degree/ 45degree = 8.

QUESTION: 10

State the name of a regular polygon of 5 sides.

Solution:

Pentagon have 5 sides .

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