Question

name ______
show all steps!!
figures are not drawn to scale!
use the figure at the right to answer problems 1 - 8
classify each pair of angles as one of the following:
a. alternate interior angles b. corresponding angles
c. alternate exterior angles d. vertical angles
e. linear pair f. same side interior
g. same side exterior h. none of the above

1. __ <9 & <16 2. <15 & <11 3. <10 & <15 4. __ <12 & <15
2. __ <9 & <11 6. <9 & <15 7. <13 & <16 8. __ <14 & <11

Explanation:

Step1: Recall angle pair definitions

1. Alternate Interior: Inside parallel lines, opposite sides of transversal
2. Corresponding: Same relative position on parallel lines/transversal
3. Alternate Exterior: Outside parallel lines, opposite sides of transversal
4. Vertical: Opposite, formed by intersecting lines
5. Linear Pair: Adjacent, sum to $180^\circ$
6. Same Side Interior: Inside parallel lines, same side of transversal
7. Same Side Exterior: Outside parallel lines, same side of transversal

Step2: Classify ∠9 & ∠16

∠9 (exterior left) & ∠16 (exterior right, opposite side of transversal) → Alternate Exterior Angles

Step3: Classify ∠15 & ∠11

∠15 (interior right) & ∠11 (interior right, same relative position) → Corresponding Angles

Step4: Classify ∠10 & ∠15

∠10 (interior left) & ∠15 (interior right, same side of transversal) → Same Side Interior Angles

Step5: Classify ∠12 & ∠15

∠12 & ∠15 are adjacent, form a straight line → Linear Pair

Step6: Classify ∠9 & ∠11

∠9 (exterior left) & ∠11 (interior right, opposite side of transversal) → None of the above

Step7: Classify ∠9 & ∠15

∠9 (exterior left) & ∠15 (interior right, same side of transversal) → Same Side Exterior Angles

Step8: Classify ∠13 & ∠16

∠13 & ∠16 are opposite, formed by intersecting lines → Vertical Angles

Step9: Classify ∠14 & ∠11

∠14 (interior left) & ∠11 (interior right, opposite side of transversal) → Alternate Interior Angles

Answer:

1. C. alternate exterior angles
2. B. corresponding angles
3. F. same side interior
4. E. linear pair
5. H. none of the above
6. G. same side exterior
7. D. vertical angles
8. A. alternate interior angles