Question

#3.) in the diagram below l || m.
fill in the chart below:
angles angle pair name relationship
**∠2 and ∠12
**∠5 and vertical angles
*∠7 and alternate interior angles
∠10 and ∠11
∠8 and ∠16
**∠15 and same side exterior angles
#4.) in the diagram below ab || cd.
fill in the chart below:
angle pair name angles relationship
**same side interior angles ∠bgh and
same side exterior angles ∠bge and
alternate interior angles ∠agh and
alternate exterior angles ∠chf and
*corresponding angles ∠chg and

Explanation:

Step1: Recall angle - pair definitions

Use the properties of parallel lines and transversals to identify angle - pairs.

Step2: Analyze ∠2 and ∠12

∠2 and ∠12 are corresponding angles. Corresponding angles are congruent when two parallel lines are cut by a transversal.

Step3: Find vertical angles for ∠5

Vertical angles are opposite each other when two lines intersect. The vertical angle of ∠5 is ∠7.

Step4: Find alternate - interior angles for ∠7

Alternate - interior angles are between the two parallel lines and on opposite sides of the transversal. The alternate - interior angle of ∠7 is ∠10.

Step5: Analyze ∠10 and ∠11

∠10 and ∠11 are adjacent angles. They share a common side and a common vertex.

Step6: Analyze ∠8 and ∠16

∠8 and ∠16 are corresponding angles.

Step7: Find same - side exterior angles for ∠15

The same - side exterior angle of ∠15 is ∠3.

Step8: For the second part, analyze same - side interior angles for ∠BGH

The same - side interior angle of ∠BGH is ∠GHD.

Step9: Analyze same - side exterior angles for ∠BGE

The same - side exterior angle of ∠BGE is ∠EHD.

Step10: Analyze alternate - interior angles for ∠AGH

The alternate - interior angle of ∠AGH is ∠GHC.

Step11: Analyze alternate - exterior angles for ∠CHF

The alternate - exterior angle of ∠CHF is ∠AGE.

Step12: Analyze corresponding angles for ∠CHG

The corresponding angle of ∠CHG is ∠AGH.

Answer:

Angles	Angle Pair Name	Relationship
∠5 and ∠7	Vertical Angles	Congruent
∠7 and ∠10	Alternate Interior Angles	Congruent
∠10 and ∠11	Adjacent Angles	N/A
∠8 and ∠16	Corresponding Angles	Congruent
∠15 and ∠3	Same Side Exterior Angles	Supplementary
∠BGH and ∠GHD	Same Side Interior Angles	Supplementary
∠BGE and ∠EHD	Same Side Exterior Angles	Supplementary
∠AGH and ∠GHC	Alternate Interior Angles	Congruent
∠CHF and ∠AGE	Alternate Exterior Angles	Congruent
∠CHG and ∠AGH	Corresponding Angles	Congruent