Question

classify ∠1 and ∠2 on the diagram as consecutive (same - side) interior, or consecutive (same - side) exterior angles.
3.
diagram of two lines and a transversal with ∠1 and ∠2
4.
diagram of two lines and a transversal with ∠1 and ∠2, with corresponding written below
5.
diagram of two lines and a transversal with ∠1 and ∠2
6.
diagram of two lines and a transversal with ∠1 and ∠2, with some hand - written text below
7.
diagram of two lines and a transversal with ∠1 and ∠2
8.
diagram of two lines and a transversal with ∠1 and ∠2
© gina wilson (all things algebra) © 2014 - 2019

Explanation:

Step1: Analyze Diagram 3

Identify the transversal and parallel lines. ∠1 and ∠2 are on the same side of the transversal, between the two lines (interior). So they are consecutive (same - side) interior angles.

Step2: Analyze Diagram 4

Check the positions. ∠1 and ∠2 are in corresponding positions relative to the transversal and the two lines (same relative position at each intersection), so they are corresponding angles (matches the written "corresponding").

Step3: Analyze Diagram 5

Look at the angles' positions. ∠1 and ∠2 are on the same side of the transversal, outside the two lines (exterior), so they are consecutive (same - side) exterior angles.

Step4: Analyze Diagram 6

Observe the angles. ∠1 and ∠2 are on the same side of the transversal, between the two lines (interior), so they are consecutive (same - side) interior angles (matches the written "consecutive interior").

Step5: Analyze Diagram 7

Check the angles. ∠1 and ∠2: ∠1 is above the transversal, ∠2 is below, and they are vertical or? Wait, no, the lines: one is a transversal, one is horizontal, one is slant. Wait, ∠1 and ∠2: ∠2 is a right angle? Wait, no, the horizontal line and the vertical transversal: ∠2 is a right angle, and ∠1 is adjacent? Wait, no, re - check. Wait, the two non - transversal lines: one slant, one horizontal. The transversal is vertical. ∠1 is between slant and vertical, ∠2 is between horizontal and vertical, same side of transversal, interior? Wait, no, maybe alternate interior? Wait, no, the diagram 7: ∠1 and ∠2, the transversal is vertical, the two lines are slant (top) and horizontal (bottom). ∠1 is above horizontal, below slant? Wait, maybe they are corresponding? No, wait, the horizontal line and the slant line: the transversal is vertical. ∠1 and ∠2: ∠2 is a right angle (horizontal and vertical), ∠1 is at the slant and vertical. Wait, maybe they are same - side interior? No, maybe alternate exterior? Wait, perhaps I made a mistake. Wait, the key is to use the definitions: consecutive interior (same side, between lines), consecutive exterior (same side, outside lines), corresponding (same position), alternate interior (opposite sides, between lines), alternate exterior (opposite sides, outside lines). For diagram 7, let's re - examine: the two lines (non - transversal) are a slant line (going up - left to down - right) and a horizontal line (left - right). The transversal is vertical (up - down). ∠1 is at the intersection of slant and vertical, above the slant line? Wait, no, the slant line is going from left - down to right - up? Wait, the arrows: the slant line has arrows going left - down and right - up, horizontal line left - right, vertical transversal up - down. So ∠1 is between slant (right - up) and vertical, ∠2 is between horizontal (right) and vertical, same side of transversal (right side), and between the two lines (slant and horizontal are the two lines), so consecutive (same - side) interior angles? Wait, maybe.

Step6: Analyze Diagram 8

Look at ∠1 and ∠2. They are on opposite sides of the transversal, outside the two lines? No, the two non - transversal lines are both going up (left and right). The transversal is a slant line. ∠1 and ∠2 are in alternate positions relative to the transversal, outside the two lines? Wait, no, the two lines are close, the transversal crosses them. ∠1 is at the left line and transversal, ∠2 is at the right line and transversal, opposite sides of transversal, outside the two lines? No, the two lines are parallel? Maybe alternate exterior? Or corresponding? Wait, no, the positions: ∠1 and ∠2 are in corresponding positions? No, opposite sides. Wait, maybe alternate interior? No, outside. Wait, perhaps they are alternate exterior angles.

But since the question is to classify, let's summarize each:

Diagram 3: Consecutive (same - side) interior angles.

Diagram 4: Corresponding angles.

Diagram 5: Consecutive (same - side) exterior angles.

Diagram 6: Consecutive (same - side) interior angles.

Diagram 7: Let's re - check. The horizontal line and the slant line (going left - down to right - up), transversal vertical. ∠1 is above the horizontal line, ∠2 is below? No, ∠2 is on the horizontal line (left - right) and vertical transversal, so ∠2 is a right angle (if horizontal and vertical are perpendicular). ∠1 is at slant and vertical, above the slant line? Wait, maybe ∠1 and ∠2 are same - side interior? No, maybe they are corresponding? Wait, the slant line and horizontal line: the transversal is vertical. ∠1 is at (slant, vertical) top - right, ∠2 is at (horizontal, vertical) top - right? No, horizontal is left - right, so ∠2 is at (horizontal, vertical) right - side, ∠1 is at (slant, vertical) right - side, same position, so corresponding? Wait, maybe.

Diagram 8: ∠1 and ∠2 are on opposite sides of the transversal, outside the two lines (the two vertical - like lines? No, the two lines are slant? Wait, the two lines (non - transversal) are both going up (left line: up - down, right line: up - down with a slant at the end? No, the diagram 8: two lines, one on left (vertical - like, arrow down), one on right (slant, arrow down - right). The transversal is a slant line (left - up to right - down). ∠1 is at left line and transversal, ∠2 is at right line and transversal, opposite sides of transversal, outside the two lines? No, between? Wait, no, the two lines (left and right) are not parallel. Wait, maybe alternate exterior?

But the main task is to classify each ∠1 and ∠2. Let's take diagram 3 as an example:

For diagram 3:
- Step1: Identify the two lines (the two horizontal - like lines, one top, one bottom) and the transversal (the vertical line).
- Step2: ∠1 is between the two lines, above the bottom line, below the top line, on the right side of the transversal.
- Step3: ∠2 is also between the two lines, below the top line, above the bottom line, on the right side of the transversal.
- Step4: So they are on the same side of the transversal, between the two lines → consecutive (same - side) interior angles.

Answer:

• Diagram 3: Consecutive (same - side) interior angles
• Diagram 4: Corresponding angles
• Diagram 5: Consecutive (same - side) exterior angles
• Diagram 6: Consecutive (same - side) interior angles
• Diagram 7: Corresponding angles (or same - side interior, depending on exact line positions)
• Diagram 8: Alternate exterior angles (or corresponding, depending on exact line positions)

(Note: The exact classification depends on precise line orientations, but the above is based on standard angle - pair definitions.)