Lines and Angles

Lines and angles

What is a linear pair?

A linear pair is a pair of angles that share a side and a base. In other words, they are the two angles created along one line when two lines intersect. Linear pairs are always supplementary.

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Thus, ∠​ ABD and ________ form a linear pair, and since ABC is a straight line, the sum of angles in the linear pair is ________

What is a vertically opposite angle?

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other. Also, a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees.

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 For example, if two lines intersect and make an angle, say X= $45\degree$  , then its opposite angle is also equal to __________ And the angle adjacent to angle X will be equal to 180 - _____ = ________

^{Two or more lines which share exactly one common point are called intersecting lines. This common point exists on all these lines and is called the point of intersection}

• The intersecting lines meet at one, and only one point, no matter at what angle they meet.

• No two straight lines can meet at more than one point.

• The lines that meet at more than one point are not straight lines. At least one of them is a curve

Let us take a few examples

Intersecting lines

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Lines AB and CD

intersect at point: _______

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∠1 is vertically opposite to ∠____

∠2 is vertically opposite to ∠____

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 $\angle1$  is an adjacent angle with  $\angle$  ____.
So,  $\angle1\ and\ \angle2$  forms a _____ pair of angles

Multiple Select

In the figure, if  $\angle1=45\degree$  , then the angle adjacent to it will be  $\angle2\ =180\degree-\angle1$   $\Longrightarrow$   $\angle2=180\degree-\angle$  __ $\degree=$  ___ $\degree$ 
And  $\angle3=180\degree-\angle2\Longrightarrow\angle3=180\degree-\angle$  __ $\degree=$  ___ $\degree$  

•  $\angle1=45\degree,\angle2=135\degree,\angle3=45\degree$  

•  $\angle1=45\degree,\angle2=45\degree,\angle3=135\degree$  

•  $\angle1=45\degree,\angle2=135\degree,\angle3=135\degree$  

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 $\ \angle1=\angle3\ =\ldots\degree\ and\ \angle2=\angle4=\ldots\degree$  

So , we say vertical opposite angles are always equal

•  $\angle1=\angle3$  

•  $\angle2=\angle4$  

Two or more lines that do not intersect each other are called non-intersecting lines. It is to be noted that:

• Non-intersecting lines can never meet

• They are also known as the parallel lines.

• They are always at the same distance from one another. This is called the distance between two parallel lines.

Few examples of non intersecting lines

Parallel Lines

Multiple Select

Identify the Parallel and Intersecting pair of lines in the given figure.

• ML || NO

• MN || LO

• ML ∦ NO

• MN ∦ LO

Consider two lines, AB and CD. Let  $\overline{xy}$ be the line that intersects these two lines at two distinct points, P and Q

• A line that intersects two other lines at two distinct points is known as the transversal to the lines. In Fig.B,  $\overline{xy}$  is the transversal.

Corresponding angles

• ∠AXP , ∠CYP

  
  

• ∠AXQ , ∠CYQ

Multiple Select

Find the other pair of corresponding angles

• ∠PXB , ∠CYQ

• ∠BXQ , ∠DYQ

• ∠PXB , ∠QYD

• ∠PXB , ∠PYD

Alternate Interior Angles

•  $\angle$  AMY, $\angle$  DNX

• 
  

Multiple Select

Find the other pair of alternate interior angle

• $\angle BMY$

• $\angle AMX$

• $\angle CNX$

• $\angle CNX$

Alternate exteriror angles

• They lie on alternate sides of the transversal

• They lie on the exterior to the lines

•  $\angle AXJ\ ,\angle DYK$  

Multiple Select

Find the other pair of alternate exterior angle

• $\angle BMY$

•  $\angle JXB$ 

•  $\angle KYC$ 

• $\angle CNX$