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, the horizontal line is the transversal.

Step2: Define corresponding angles

Corresponding angles are in the same relative position.
Corresponding - angle pairs: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$.

Step3: Define alternate - interior angles

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

Step4: Define alternate - exterior angles

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

Step5: Define consecutive - interior angles

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

Step6: Define consecutive - exterior angles

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

Answer:

a) The transversal is the horizontal line.
b) Corresponding angles: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$.
c) Alternate - interior angles: $\angle3$ and $\angle5$, $\angle4$ and $\angle6$.
d) Alternate - exterior angles: $\angle1$ and $\angle7$, $\angle2$ and $\angle8$.
e) Consecutive - interior angles: $\angle3$ and $\angle6$, $\angle4$ and $\angle5$.
f) Consecutive - exterior angles: $\angle1$ and $\angle8$, $\angle2$ and $\angle7$.