Question

5 in the diagram from the previous activity, each time you extended a side of the triangle, you created a transversal. identify the angle pairs described by each statement.
take note...
same - side interior angles are on the same side of the transversal and are between the other two lines.
same - side exterior angles are on the same side of the transversal and are outside the other two lines.
(a) corresponding angles when \\( \overleftrightarrow { b c } \\) is the transversal
(b) alternate interior angles when \\( \overleftrightarrow { b c } \\) is the transversal
(c) alternate exterior angles when \\( \overleftrightarrow { a b } \\) is the transversal
(d) same - side interior angles when \\( \overleftrightarrow { a b } \\) is the transversal
(e) same - side exterior angles when \\( \overleftrightarrow { a b } \\) is the transversal

Explanation:

Step1: Recall the definitions of angle pairs

• Corresponding angles: Angles in the same relative position.
• Alternate interior angles: Non - adjacent interior angles on opposite sides of the transversal.
• Alternate exterior angles: Non - adjacent exterior angles on opposite sides of the transversal.
• Same - side interior angles: Interior angles on the same side of the transversal.
• Same - side exterior angles: Exterior angles on the same side of the transversal.

Step2: Analyze each part

• a) When \(\overleftrightarrow{BC}\) is the transversal, corresponding angles are \(\angle ICH\) and \(\angle CBG\), \(\angle ACI\) and \(\angle CBF\)
• b) When \(\overleftrightarrow{BC}\) is the transversal, alternate interior angles are \(\angle BCA\) and \(\angle CBF\)
• c) When \(\overleftrightarrow{AB}\) is the transversal, alternate exterior angles are \(\angle JAB\) and \(\angle EBG\)
• d) When \(\overleftrightarrow{AB}\) is the transversal, same - side interior angles are \(\angle BAC\) and \(\angle ABC\)
• e) When \(\overleftrightarrow{AB}\) is the transversal, same - side exterior angles are \(\angle JAB\) and \(\angle DBG\)

Answer:

a. \(\angle ICH\) and \(\angle CBG\), \(\angle ACI\) and \(\angle CBF\)
b. \(\angle BCA\) and \(\angle CBF\)
c. \(\angle JAB\) and \(\angle EBG\)
d. \(\angle BAC\) and \(\angle ABC\)
e. \(\angle JAB\) and \(\angle DBG\)