Question

1
drag the tiles to the boxes to form correct pairs

in the diagram, transversal ( t ) cuts across the parallel lines ( a ) and ( b ). match the pairs of angles with the relationship that shows they are congruent.
alternate exterior angles ( angle 2, angle 3 ) and ( angle 5, angle 8 ) alternate interior angles
( angle 1, angle 8 ) and ( angle 2, angle 7 ) corresponding angles ( angle 3, angle 6 ) and ( angle 4, angle 5 )
vertical angles ( angle 1, angle 5 ) and ( angle 2, angle 6 )

Explanation:

Step1: Recall the definition of alternate exterior angles

Alternate exterior angles are non - adjacent exterior angles that lie on opposite sides of the transversal.
For the given parallel lines \(a\) and \(b\) cut by transversal \(t\), \(\angle1,\angle8\) and \(\angle2,\angle7\) are alternate exterior angles.

Step2: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal.
For the given parallel lines \(a\) and \(b\) cut by transversal \(t\), \(\angle3,\angle6\) and \(\angle4,\angle5\) are alternate interior angles.

Step3: Recall the definition of corresponding angles

Corresponding angles are angles that are in the same relative position with respect to the parallel lines and the transversal.
For the given parallel lines \(a\) and \(b\) cut by transversal \(t\), \(\angle1,\angle5\) and \(\angle2,\angle6\) are corresponding angles.

Step4: Recall the definition of vertical angles

Vertical angles are pairs of opposite angles formed by two intersecting lines.
For the given parallel lines \(a\) and \(b\) cut by transversal \(t\), \(\angle2,\angle3\) and \(\angle5,\angle8\) are vertical angles.

Answer:

• alternate exterior angles: \(\angle1,\angle8\) and \(\angle2,\angle7\)
• alternate interior angles: \(\angle3,\angle6\) and \(\angle4,\angle5\)
• corresponding angles: \(\angle1,\angle5\) and \(\angle2,\angle6\)
• vertical angles: \(\angle2,\angle3\) and \(\angle5,\angle8\)