Question

1. use the diagram below to answer the following questions. a) name a transversal. b) name all corresponding angles. c) name all alternate interior angles. d) name all alternate exterior angles. e) name all consecutive interior angles. f) name all consecutive exterior angles.

Explanation:

Step1: Identify transversal

A transversal is a line that intersects two or more other lines. In the given diagram, any of the non - parallel lines can be considered a transversal. Let's say the slanted line is the transversal.

Step2: Identify corresponding angles

Corresponding angles are in the same relative position at each intersection. They are: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$.

Step3: Identify alternate interior angles

Alternate interior angles are between the two intersected lines and on opposite sides of the transversal. They are: $\angle3$ and $\angle6$, $\angle4$ and $\angle5$.

Step4: Identify alternate exterior angles

Alternate exterior angles are outside the two intersected lines and on opposite sides of the transversal. They are: $\angle1$ and $\angle8$, $\angle2$ and $\angle7$.

Step5: Identify consecutive interior angles

Consecutive interior angles are between the two intersected lines and on the same side of the transversal. They are: $\angle3$ and $\angle5$, $\angle4$ and $\angle6$.

Step6: Identify consecutive exterior angles

Consecutive exterior angles are outside the two intersected lines and on the same side of the transversal. They are: $\angle1$ and $\angle7$, $\angle2$ and $\angle8$.

Answer:

a) A transversal: The slanted line (any non - parallel line can be chosen as a transversal)
b) Corresponding angles: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$
c) Alternate interior angles: $\angle3$ and $\angle6$, $\angle4$ and $\angle5$
d) Alternate exterior angles: $\angle1$ and $\angle8$, $\angle2$ and $\angle7$
e) Consecutive interior angles: $\angle3$ and $\angle5$, $\angle4$ and $\angle6$
f) Consecutive exterior angles: $\angle1$ and $\angle7$, $\angle2$ and $\angle8$