## Topic outline

• ### # Mathematics - Class 5 / Grade 5

• Quadrilateral means "four sides" (quad means four, lateral means side).So, A closed figure made up of four line segments is called a quadrilateral. It is 2-dimensional (a flat shape) closed (the lines join up) figure made up of 4 straight lines.

The below figure is called a quadrilateral. It can be named in the following ways: ABCD or BCDA or CDAB or DABC Parts or Elements of a Quadrilateral

1.   Four points A, B, C, D are called its vertices.

2.   Four line segments AB, BC, CD and DA are called its sides.

3.   DAB, ABC, BCD and CDA are called its angles, and can also be written as A, B, C and D respectively. Angles are four in total.

4.   The two Line segments AC and BD are called its diagonals. (A line segment joining a pair of opposite vertices is called a diagonal.)

5.   The interior angles add up to 360 degrees.

Parallelogram A quadrilateral is parallelogram whose opposite sides are parallel and equal in length. Also its opposite angles are equal. Example: rectangle, square and rhombus.

Here, ABCD is a parallelogram and

a.   AB DC and AD BC.

b.   AB = DC; AD = BC

c.   A = C; B = D

Rectangle A rectangle is a parallelogram in which opposite sides are equal in length and each angles measure 90°.

Here, ABCD is a rectangle and

b.   AD = BC; AB = DC

c.   A = B = C = D = 90°

Square A square is a parallelogram in which all sides are equal in length and each angle measure 90°. It is a rectangle in which all sides are equal.

Here, ABCD is a square and

b.   AB = BC = CD = DA

c.   A = B = C = D = 90°

Rhombus A rhombus is a parallelogram whose all sides are equal. A rhombus is sometimes called a diamond.

Here, ABCD is a rhombus and

b.   AB = BC = CD = DA

c.   A = C  and B = D (opposite angles are equal)

Trapezium A trapezium is a quadrilateral which has a pair of opposite sides parallel.

Here, ABCD is a trapezium and AB DC

Note: If a trapezium has non parallel sides equal, it is called isosceles trapezium. Here, ABCD is a isosceles trapezium and

b.   AB = BC

Sum of Angles of a Quadrilateral Let us join the opposite vertices of a quadrilateral ABCD.

Now we see two triangles in this figure.

We know that the sum of the angles of a triangle = 180°

As there are two triangles, therefore, the sum of angles of two triangles is 180° + 180° = 360°

So, sum of the angles of a quadrilateral = 360°

Note: No matter what the shape of quadrilateral is, the sum of four angles of a quadrilateral is 360°

Example 1: In a quadrilateral ABCD, A = 80°, B = 105° and C = 115°. Find D.

Solution: We know that the sum of four angles of a quadrilateral ABCD is 360°

Or A + B + C + D = 360°

80° + 105° + 115° + D = 360°

300° + D = 360°

D = 360° – 300° = 60°

Example 2: Find the measure of the missing angles in a parallelogram, if A = 60°.

Solution: We know that the opposite angles of a parallelogram are equal, so, C will also measure 60°.

Sum of angles of a quadrilateral = 360°

Or A + B + C + D = 360°

60° + B + 60° + D = 360° (As A = C)

B + D + 120° = 360°

B + D = 360° – 120° = 240°

But B = D (as opposite angles of a parallelogram are equal)

B = D = 240°/2 = 120°

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