Question

main areas/questions notes/examples
parallel lines
& transversals.
diagram of parallel lines and transversal

• two lines that ____________ are called parallel lines.
• arrows on lines indicate that they are parallel.
• symbol for parallel: ________
• a line that __________ or __________ is called a transversal.
• in the diagram to the left, ______ and the transversal is ______.

special
angle pairs
diagrams of special angle pairs with parallel lines and transversal
corresponding angles are in the same position on the parallel lines in relation to the transversal. these angles are always ________.
alternate interior angles are inside the parallel lines and on opposite sides of the transversal. these angles are always ________.
alternate exterior angles are outside the parallel lines and on opposite sides of the transversal. these angles are always ________.
consecutive interior angles are on the same side of the transversal and inside the parallel lines. these angles are always ________.
practice classifying
diagram for angle classification practice
directions: using the diagram to the left, classify each angle pair and indicate whether they are congruent or supplementary.

1. ∠1 and ∠5 \t2. ∠6 and ∠8
2. ∠2 and ∠3 \t4. ∠3 and ∠7
3. ∠2 and ∠4 \t6. ∠6 and ∠7
4. ∠2 and ∠6 \t8. ∠4 and ∠8

Explanation:

1. $\boldsymbol{\angle 1}$ and $\boldsymbol{\angle 5}$

Step1: Identify Angle Pair Type

$\angle 1$ and $\angle 5$ are in the same position relative to the parallel lines (assumed from the diagram context) and the transversal. So, they are corresponding angles.

Step2: Determine Congruence/Supplementarity

Corresponding angles formed by parallel lines and a transversal are congruent.

Step1: Identify Angle Pair Type

$\angle 6$ and $\angle 8$ are vertical angles (opposite angles formed by intersecting lines) or also, in the context of parallel lines, they can be seen as vertical angles. But also, if we consider the parallel lines, they are vertical angles. However, another way: $\angle 6$ and $\angle 8$ are vertical angles, and vertical angles are congruent. Also, if we consider the parallel lines, they can be alternate interior? Wait, no. Wait, $\angle 6$ and $\angle 8$: let's see, if the lines are parallel, and the transversal, but actually, $\angle 6$ and $\angle 8$ are vertical angles (formed by the intersection of two lines). Vertical angles are congruent. Also, if we consider the parallel lines, $\angle 6$ and $\angle 8$: wait, maybe alternate interior? No, better: vertical angles. But also, in the parallel lines context, $\angle 6$ and $\angle 8$: let's re - check. Wait, $\angle 6$ and $\angle 8$: if the two lines are parallel, and the transversal, but actually, $\angle 6$ and $\angle 8$ are vertical angles (formed by the intersection of the two lines, not the transversal and parallel lines). Wait, no, maybe I made a mistake. Wait, the diagram for practice has two intersecting lines? Wait, no, the practice diagram has two lines (c and d) intersected by a transversal? Wait, no, the practice diagram shows two lines (c and d) intersecting, and a transversal? Wait, maybe the practice diagram is of two parallel lines? Wait, the problem says "using the diagram to the left" (the practice diagram). Assuming the lines are parallel (as per the topic), $\angle 6$ and $\angle 8$: wait, $\angle 6$ and $\angle 8$ are vertical angles? No, wait, $\angle 6$ and $\angle 8$: if we have two parallel lines and a transversal, but in the practice diagram, maybe it's two intersecting lines? Wait, no, the main topic is parallel lines and transversals. So, let's correct. $\angle 6$ and $\angle 8$: in the parallel lines and transversal context, $\angle 6$ and $\angle 8$ are vertical angles? No, wait, $\angle 6$ and $\angle 8$: let's see, $\angle 6$ and $\angle 8$ are vertical angles (formed by the intersection of the two lines, not the transversal and parallel lines). Wait, no, maybe the practice diagram has two parallel lines cut by a transversal, and another line? Wait, maybe I mis - see. Alternatively, $\angle 6$ and $\angle 8$: if we consider the two parallel lines (from the main topic) and the transversal, $\angle 6$ and $\angle 8$: wait, $\angle 6$ and $\angle 8$ are vertical angles (formed by the intersection of the two lines, not the transversal and parallel lines). Wait, no, maybe the practice diagram is of two parallel lines cut by a transversal, and $\angle 6$ and $\angle 8$ are vertical angles? No, vertical angles are formed by intersecting lines. Wait, maybe $\angle 6$ and $\angle 8$ are alternate interior angles? No, alternate interior angles are inside the parallel lines. Wait, $\angle 6$ and $\angle 8$: let's think again. If the two lines are parallel, and the transversal, then $\angle 6$ and $\angle 8$: if $\angle 6$ is on one parallel line, and $\angle 8$ is on the other, and they are on opposite sides of the transversal? No, maybe $\angle 6$ and $\angle 8$ are vertical angles. Vertical angles are congruent. So, angle pair: Vertical Angles (or also, in the parallel lines context, maybe alternate interior? No, vertical angles are more accurate here). So, relationship: Congruent.

Step2: Determine Congruence/Supplementarity

Vertical angles are congruent. Also, if we consider the parallel lines, but in this case, a…

Step1: Identify Angle Pair Type

$\angle 2$ and $\angle 3$ are adjacent angles forming a linear pair (they are on a straight line, formed by the intersection of two lines). A linear pair of angles is supplementary (their sum is $180^{\circ}$).

Step2: Determine Congruence/Supplementarity

Linear pair angles are supplementary.

Answer:

Angle Pair: Corresponding Angles, Relationship: Congruent

2. $\boldsymbol{\angle 6}$ and $\boldsymbol{\angle 8}$