Congruent Quadrilaterals

By Author: math qa22
Total Articles: 69
Comment this article

Congruent quadrilaterals are quadrilaterals that are exactly the same (have the same lengths of sides, angles etc). Congruent quadrilaterals could also be in different positions and rotated, but as long as the sides and angles are the same, they are still congruent.
Similar means that the shapes have the same angles, but the lengths of the sides won’t be the same (one would be a lot bigger than the other).

Congruent Quadrilateral 2

These figure shows that the quadrilaterals are congruent.
Congruent Quadrilateral( Types)

Quadrilateral just means "four sides"
(quad means four, lateral means side).

Any four-sided shape is a Quadrilateral.

But the sides have to be straight, and it has to be 2-dimensional.

Quadrilaterals

Properties

Four sides (or edges)
Four vertices (or corners).
The interior angles add up to 360 degrees.

Quadrilaterals 2

Congruent Quadrilateral( Properties)

Properties of Parallelograms

In a parallelogram,

1. The parallel sides are parallel by definition.

2. The opposite sides are congruent.

3. ...
... The opposite angles are congruent.

4. The diagonals bisect each other.

5. Any pair of consecutive angles are supplementary.

Properties of Rectangles

In a rectangle,

1. All the properties of a parallelogram apply by definition.

2. All angles are right angles.

3. The diagonals are congruent.

Properties of Rhombuses

In a rhombus,

1. All the properties of a parallelogram apply by definition.

2. Two consecutive sides are congruent by definition.

3. All sides are congruent.

4. The diagonals bisect the angles.

5. The diagonals are perpendicular bisectors of each other.

6. The diagonals divide the rhombus into four congruent right triangles.

Properties of Squares

In a square,

1. All the properties of a rectangle apply by definition.

2. All the properties of a rhombus apply by definition.

3. The diagonals form four isosceles right triangles

If two four sided figures are satisfying the same pair of properties then they are said to be

Quadrilateral and if they have same length of corresponding sides and same measure of

corresponding angles & also the other properties to be same then those quadrilateral are

congruent to each other.

In this article we shall deal with solving area for quadrilaterals, before learning area formula for quadrilaterals we should know about quadrilateral. Quadrilateral is a four sided polygon, the sides of quadrilaterals are closed four line segments. To calculate area of a quadrilateral we have to know length, base and height other wise we know the sides of a quadrilaterals. The area of a triangle is measured in terms of square units. The following are the examples involved in solve area formulas for quadrilaterals.

Check this Volume of a Triangular Prism awesome i recently used to see.

Learn formulas for quadrilaterals:

Area of a quadrilaterals

The quadrilateral consists of different types, quadrilaterals such as square, rectangle, parallelogram, rhombus, trapezoid and kite. Formulas for area of these quadrilateral are given below.

Area of a square = s2, s is side of the square.

Area of rectangle = l × w, where l and w are the length and width of the rectangle.

Area of parallelogram = bh, b and h are the base and height of the parallelogram.

Area of rhombus =bh, b and h are the base and height of the rhombus.

Area of a trapezoid =1/2 (a+b)h, a and b are the parallel base and h is the height.

Area of a kite = 1/2 (d1 × d2), Where d1 and d2 are diagonals of the kite.

Area of any quadrilateral is given by

Area = sqrt({(s-a)(s-b)(s-c)(s-d) -1/4(ac+bd+pq)(ac+bd-pq)})

where a,b,c and d are sides of the quadrilateral. P and Q are the diagonals of the quadrilaterals.

S is the perimeter of the quadrilateral.

s = (a+b+c+d)/2

Let us we solve problem for area of quadrilateral.

Example:

Solve the area of a quadrilateral whose sides are 10cm, 20cm, 30cm and 40cm and its diagonals are 15cm and 25cm?

Solution:

Given: a = 10cm, b= 20cm, c = 30cm, d = 40cm, p = 15cm, q = 25cm

s = (10+20+30+40)/2

= 100/2 = 50

Area = sqrt({(s-a)(s-b)(s-c)(s-d) -1/4(ac+bd+pq)(ac+bd-pq)})

= sqrt( {(50-10)(50-20)(50-30)(50-40) -1/4(10xx30+20xx40+15xx25)(10xx30+20xx40-15xx25)})

= sqrt( {(40)(30)(20)(10) -1/4(300+800+375)(300+800-375)})

= sqrt((240000)-1/4(1475)(725))

= sqrt(240000 - 267343.75)

= v-27343.75

= 165.36cm2
Solve Examples to Area Formulas for Quadrilaterals:

Example 1:

Solve the area of a square whose side 7cm?

Solution:

Given: side = 7cm

Area of a square = s2

= 72

= 49cm2

Example 2:

Solve the area of a rectangle whose length and width are 7cm and 5cm?

Solution:

Area of a rectangle = l×w

= 7 × 5

= 35cm2

Example 3:

Solve the area of a Kite whose diagonal are 14cm and 10cm?

Solution:

Area of the kite = 1/2 (d1 × d2)

= 1/2 (14 × 10)

= 1/2 (140)

= 70cm2

Learn more on about Exponential Function Examples and its Examples. Between, if you have problem on these topics Exponential Function Graphs, Please share your comments.