Math 10 5.5A

Two lines intersect to form

 $\angle1,\ \angle2,\ \angle3,\ and\ \angle4.$  
Name a Linear Pair

•  $\angle2\ and\ \angle4$  

•  $\angle5\ and\ \angle4$  

•  $\angle1\ and\ \angle2$  

•  $\angle1\ and\ \angle3$  

Since  $\angle1\ and\ \angle2$  form a Linear Pair, 

•  $\angle1\ and\ \angle2$  are both obtuse angles.
  

•   $m\angle1+m\angle2=180\degree.$  

•  $\angle1\ and\ \angle2$  are both acute angles.

• the lines are perpendicular (they form a right angle).

Name a different Linear Pair of angles that includes  $\angle1.$  

•  $\angle1\ and\ \angle4$ 
  

•   $\angle1\ and\ \angle2$  

•  $\angle1\ and\ \angle3$  are both acute angles.

•  $\angle1\ and\ \angle1.$  

Since  $\angle1\ and\ \angle4$  form a Linear Pair of Angles,

• the lines are parallel.

•   $m\angle1+m\angle3=180\degree.$  

•  $\angle1\ and\ \angle4$  are both acute angles.

•  $m\angle1+m\angle4=180\degree.$  
  

Since  $m\angle2+m\angle1=180\degree$  and  $m\angle4+m\angle1=180\degree$  , then

• the lines are perpendicular.

•   $m\angle1+m\angle3=180\degree.$  

•  $m\angle2+m\angle1=m\angle4+m\angle1$  
  

•  $\angle2\ and\ \angle4$  must be right angles 
  

If  $m\angle2+m\angle1=m\angle4+m\angle1$  and we subtract  $m\angle1$  from both sides,

•  $m\angle2=30\degree$  
  

•   $m\angle2+m\angle4=m\angle6$  

•  $m\angle2=m\angle4\ and\ \angle2\cong\angle4!$  
  

•  $\angle2\ and\ \angle4$  must be right angles 
  

By similar reasoning, we conclude that vertical angles are congruent!  Hence

•  $\angle1\cong\angle1$   
  

•   $\angle1\cong\angle4$  

•  $\angle2\cong\angle3$  
  

•  $\angle1\cong\angle3$  
  

What is true in this picture?

• $\angle4\$ is an interior angle.

• $\angle4$ is an exterior angle.

• $\angle1$ is a right angle.

• This triangle must be isoceles.

Click all interior angles of the triangle below

•  $\angle2$ 

•  $\angle4$ 

• $\angle1$

•  $\angle3$  

 $m\angle1+m\angle2+m\angle3=$  

•  $360\degree$  

•  $90\degree$  
  

•  $270\degree$  
  

•  $180\degree$