Question

1. define the terms below. sketch an example.

a. translation
b. reflection
c. rotation

1. define the terms below: sketch an example.

a. corresponding angle
b. alternate exterior angle
c. alternate interior angle

Explanation:

1. Translation: A translation is a transformation that slides a figure from one position to another without changing its size, shape, or orientation. Example: Moving a triangle horizontally or vertically.

Reflection: A reflection is a transformation that flips a figure over a line of reflection. The resulting figure is a mirror - image of the original. Example: Flipping a triangle over a vertical line.
Rotation: A rotation is a transformation that turns a figure around a fixed point called the center of rotation. Example: Turning a triangle around a point by a certain angle.

1. Corresponding angle: When two parallel lines are cut by a transversal, corresponding angles are in the same relative position at each intersection. For example, if we have two parallel lines \(l_1\) and \(l_2\) and a transversal \(t\), the angles in the same "corner" at each intersection of \(l_1\), \(l_2\) and \(t\) are corresponding angles.

Alternate exterior angle: When two parallel lines are cut by a transversal, alternate exterior angles are the non - adjacent angles that lie outside the two parallel lines and on opposite sides of the transversal.
Alternate interior angle: When two parallel lines are cut by a transversal, alternate interior angles are the non - adjacent angles that lie between the two parallel lines and on opposite sides of the transversal.

Answer:

1.
a. Definition: A transformation that slides a figure. Example: Sliding a triangle.
b. Definition: A transformation that flips a figure over a line. Example: Flipping a triangle over a line.
c. Definition: A transformation that turns a figure around a point. Example: Turning a triangle around a point.
2.
a. Definition: Angles in the same relative position when two parallel lines are cut by a transversal. Example: Angles in the same “corner” at intersections of parallel lines and a transversal.
b. Definition: Non - adjacent angles outside two parallel lines and on opposite sides of a transversal. Example: Appropriate angles formed by parallel lines and a transversal outside the parallel lines.
c. Definition: Non - adjacent angles between two parallel lines and on opposite sides of a transversal. Example: Appropriate angles formed by parallel lines and a transversal between the parallel lines.