Math 10 5.5B

In this picture, two parallel lines are cut by a third line, called a transversal. How many vertical angle pairs can you find?

• 2 pairs of vertical angles

• 3 pairs of vertical angles

• 4 pairs of vertical angles

• 8 pairs of vertical angles

Tags

CCSS.HSG.CO.C.9

In this picture, two parallel lines are cut by a third line, called a transversal. What is the maximum number of Linear Pairs of angles you can find?

• 2 Linear Pairs

• 4 Linear Pairs

• 6 Linear Pairs

• 8 Linear Pairs

Tags

CCSS.HSG.CO.A.1

CCSS.HSG.CO.C.9

We assume that, since the lines are parallel, Corresponding Angles are congruent - for example  $\angle5\cong\angle1$  .  Check any box with Corresponding Angles.

•  $\angle1\ and\ \angle2$  
  

•  $\angle2\ and\ \angle6$  
  

•  $\angle4\ and\ \angle8$  
  

•  $\angle3\ and\ \angle7$  
  

Tags

CCSS.HSG.CO.C.9

Suppose we assume that  $\angle5\cong\angle1$ .  What is true about  $\angle1\ and\ \angle4$  ?

•  $\angle1\ and\ \angle4$  form a linear pair, so are supplementary
  

•  $\angle1\ and\ \angle4$  are adjacent angles which share a side
  

•  $\angle1\cong\ \angle4$  because they are vertical angles
  

•  $\angle1\ and\ \angle4$  are right angles
  

Tags

CCSS.HSG.CO.C.9

So, if  $\angle5\cong\angle1$ , and  $\angle4\cong\angle1$  , what can we conclude?

•  $\angle5\cong\angle4$  These are called Alternate Interior Angles.  They are congruent if they are formed by parallel lines!

• Sweet!

• Cool.

• Right on.

Tags

CCSS.HSG.CO.C.9

If  $\angle5\ and\ \angle4$  are one pair of Alternate Interior Angles, name the other pair of Alternate Interior Angles

•  $\angle3\ and\ \angle2$  

•  $\angle6\ and\ \angle8$  

•  $\angle3\ and\ \angle6$  

•  $\angle1\ and\ \angle9$  

Tags

CCSS.HSG.CO.C.9

If  $\angle5\ and\ \angle4$  and  $\angle3\ and\ \angle6$  are both pairs of Alternate Interior Angles, click any Alternate Exterior Angles below.

•  $\angle1\ and\ \angle8$  
  

•  $\angle2\ and\ \angle7$  
  

•  $\angle3\ and\ \angle2$  

•  $\angle7\ and\ \angle8$  

Tags

CCSS.HSG.CO.C.9

If these lines are parallel,  $\angle2\cong\angle6$ because they're Corresponding Angles.
What is true about  $\angle2\ and\ \angle4$  ?

• They are congruent

• They form vertical angles

• They form a linear pair

• They are non-adjacent angles

Tags

CCSS.HSG.CO.C.9

If  $\angle2\ and\ \angle4$  form a linear pair, then

•  $\angle2\cong\angle4$  
  

•  $m\angle2+m\angle4=180\degree$  
  

•  $\angle2\ and\ \angle4$  are right angles
  

• They are non-adjacent angles

Tags

CCSS.HSG.CO.C.9

If  $\angle6\cong\angle2$  then  $m\angle6=m\angle2$  .  This means that we can substitute  $m\angle6$  for  $m\angle2$  anywhere!

• Roger that!

• Huh?

Tags

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.9