Question

corresponding angles:these angles are congruent angles located on the same side of the transversal. one is in interior region and one is in exterior region at different verticeslist all pairs of corresponding angles belowalternate interior angles:these angles are congruent angles located between the parallel lines in the interior region and on opposite sides of the transversal & at different vertices.list all pairs of alternate interior angles in the diagram:alternate exterior angles:these angles are congruent angles located in the exterior region and on opposite sides of the transversal & at different vertices.list all pairs of alternate exterior angles in the diagram:exercise 2- name the following relationship between each of the following angle pairs:a) 1 and 8b) 5 and 8c) 2 and 6d) 3 and 6e) 4 and 5f) 3 and 7g) 4 and 8h) 1 and 2

Explanation:

Step1: Identify corresponding angles

Corresponding angles are on the same side of the transversal, one interior, one exterior.
Pairs: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$

Step2: Identify alternate interior angles

Alternate interior angles are between parallel lines, opposite sides of transversal.
Pairs: $\angle4$ and $\angle6$, $\angle3$ and $\angle5$

Step3: Identify alternate exterior angles

Alternate exterior angles are outside parallel lines, opposite sides of transversal.
Pairs: $\angle1$ and $\angle7$, $\angle2$ and $\angle8$

Step4: Classify angle pairs (Exercise 2)

a) $\angle1$ and $\angle8$: Alternate Exterior Angles
b) $\angle5$ and $\angle8$: Vertical Angles
c) $\angle2$ and $\angle6$: Corresponding Angles
d) $\angle3$ and $\angle6$: Alternate Interior Angles
e) $\angle4$ and $\angle5$: Alternate Interior Angles
f) $\angle3$ and $\angle7$: Corresponding Angles
g) $\angle4$ and $\angle8$: Corresponding Angles
h) $\angle1$ and $\angle2$: Linear Pair (Adjacent Supplementary Angles)

Answer:

Corresponding Angles Pairs:

$\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$

Alternate Interior Angles Pairs:

$\angle4$ and $\angle6$, $\angle3$ and $\angle5$

Alternate Exterior Angles Pairs:

$\angle1$ and $\angle7$, $\angle2$ and $\angle8$

Exercise 2:

a) Alternate Exterior Angles
b) Vertical Angles
c) Corresponding Angles
d) Alternate Interior Angles
e) Alternate Interior Angles
f) Corresponding Angles
g) Corresponding Angles
h) Linear Pair (Adjacent Supplementary Angles)