Two Parallel Lines Cut by a Transversal

Introduction to two parallel lines cut by a transversal:

Parallel lines:

Two lines on a plane that never  intersect or meet is known as parallel lines. The distance between both the lines must be the same. And they must not intercept with each other. It can also be explained as the length between parallel lines will be exactly same at any point. Examples of parallel lines are railway track, etc.

Transversal:

A straight line is said to be transversal if the line cuts two or more parallel lines at different points. In the figure the line l cuts the parallel lines a and b. So the line l is called as a transversal line

Two Parallel Lines Cut by a Transversal:

When two parallel lines are cut by a transversal then

The corresponding angles are equal

Pair of Vertically Opposite angles is equal

Pairs of Alternate interior angles are equal

Interior angles on same side are supplementary

Conditions Satisfies when Two Parallel Lines Cut by a Transversal:

The corresponding angles formed by the transversal will be equal. For example angle 4 and angle 6 are corresponding angles, and the other pairs of corresponding angles are (5 and 3), (8 and 2) and (1 and 7).

Therefore we have:               angle 6 = angle 4

angle 5 = angle 3

angle 8 = angle 2

angle 7 = angle 1

Pair of Vertically Opposite angles is equal

The pair of vertically opposite angles is equal when a transversal line is formed. For example, angle 1 and angle 3 are vertically opposite angles and the other pairs of vertically opposite angles are (2 and 4), (5 and 7) and (6 and 8).

Therefore we have:                angle 1 = angle 3

angle 2 = angle 4

angle 5 = angle 7

angle 6 = angle 8

Pairs of Alternate interior angles are equal

The pair of alternate angles is equal when the transversal line is formed. Here the pairs (2 and 6) and (3 and 7) are alternate interior angles. I have recently faced lot of problem while learning simple math problems for kids, But thank to online resources of math which helped me to learn myself easily on net.

Therefore we have:                angle 2 = angle 6

angle 3 = angle 7

Interior angles on same side are supplementary

Interior angles on same side are supplementary when a transversal is formed. The angles on the same side of the transversal are (6 and 3) and (2 and 7).

Therefore we have:                angle 3+ angle 6 = 180

angle 2 + angle 7 = 180

Radius from Circumference

Introduction to radius from circumference:
In day to day life, we often came across some unique math terms. Radius is one of the special math terms that falls under this category.

Radius of a circle is nothing but the line segment from the center of the circle to its perimeter. In other terms, half the diameter is the radius.

In this article of radius from circumference, we are going to find the radius of the circle from the circumference formula.

Formula for Radius from Circumference:

The Circumference of the circle is given by the following formula:

Circumference =  2`pi`r

If the Circumference C is given, the radius can be calculated by the following formula:

radius  =  `C/(2 pi)`

Example Problems for Finding Radius:
Example 1:

Find the radius, if the circumference of the circle is 100 cm

Solution:

Radius of circle, r  =  `C / ( 2 pi )`

=  `100 / (2 * 3.14)`

=  `100 / 6.28`

=  15.92 cm

Example 2:

Find the radius, if the circumference of the circle is 94 cm

Solution:

Radius of circle, r  =  `C / ( 2 pi )`

=  `94 / (2 * 3.14)`

=  `94 / 6.28`

=  14.97 cm

Example 3:

Find the radius, if the circumference of the circle is 60 mm

Solution:

Radius of circle, r  =  `C / ( 2 pi )`

=  `60 / (2 * 3.14)`

=  `60 / 6.28`

=  9.55 mm

Example 4:

Find the radius, if the circumference of the circle is 35 cm

Solution:

Radius of circle, r  =  `C / ( 2 pi )`

=  `35 / (2 * 3.14)`

=  `35 / 6.28`

=  5.57 cm

Example 5:

Find the radius, if the circumference of the circle is 20 mm

Solution:

Radius of circle, r  =  `C / ( 2 pi )`

=  `20 / (2 * 3.14)`

=  `20 / 6.28`

=  3.18 mm

Example 6:

Find the radius, if the circumference of the circle is 4 m

Solution:

Radius of circle, r  =  `C / ( 2 pi )`

=  `4 / (2 * 3.14)`

=  `4 / 6.28`

=  0.64 m


Practice Problems for Finding Radius:

1) Find the radius, if the circumference of the circle is 50 cm

Answer: 7.96 cm

2) Find the radius, if the circumference of the circle is 20 m

Answer: 3.18 m

3) Find the radius, if the circumference of the circle is 110 mm

Answer: 17.52 mm

4) Find the radius, if the circumference of the circle is 75 cm

Answer: 11.94 cm

5) Find the radius, if the circumference of the circle is 72 mm

Answer: 11.46 mm

Geometry Edge of Rectangular

Introduction to Geometry edge of rectangular:

Rectangular shape is one of the geometry two dimensional objects. Geom`etry edge of rectangular properties are the crossed quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals. Its angles are not right angles. Opposite sides are parallel and congruent . The diagonal bisect each other The diagonals are congruent. A four -sided plane figure with four right angles. Understanding Volume of a Rectangular Prism Formula is always challenging for me but thanks to all math help websites to help me out.

Basic Concepts of Geometry Edge of Rectangular:

Geometry edge of rectangular:

Each and every object should have edges. Two edges make the angle of geometry object.And also edges to make the corners and vertices of object .Rectangle have  four  edges and also have four vertices or corners .Each corner make the angle of 90degree.

From this diagram:

AB, BD, DC, AC are edges of the rectangle.

AB edge is parallel to CD edge

AC edge is parallel to BD edge

AB || CD, AC || BD (opposite sides are equal in rectangle)

Each edge should make the angles are


Please express your views of this topic how many edges does a rectangular prism have by commenting on blog.

Area and Perimeter of the Geometry Edge of Rectangular:

Area and perimeter:

Area of rectangle= Length * Width

Perimeter of the rectangle=2(Length + Width)

Both area and perimeter are depends on the rectangle edges.

A rectangle has two Length edges and two width edges.

Length edges are AB, CD

Width edges are BD, AC

Two length edges are equal AB=CD

Two width edges are equal BD=AC

Example problems in Geometry edge of rectangular:

1.From given diagram Find the area and perimeter of the rectangle  and name of the rectangular edges?

Solution:

Given data PQRS is closed rectangle

PQ= 13cm(PQ||SRsO P)

PQ=SR=13

QR=5.5cm(QR||PS)

So QR=PS=5.5

Length   of the rectangle=13

Width of the rectangle =5.5

Finding the area:

(1  )Area of the rectangle=Length x Width

= 13x5.5

Area =71.5cm2

(2) Finding the perimeter:

Perimeter of the rectangle=2( L+W)

=2(13+5.5)

=2(18.5)

=37cm

Perimeter=37

(3)Finding the name of the edges:

From given diagram edges are PQ,QR,RS,SP