Question

JLines AI and GJ are parallel.

Which of the following transformations would prove that the corresponding angles EBI and BCJ are congruent?
A) Translation
B) Reflection
C) Rotation
D) Dilation

Answer 1

To prove that EBI and BCJ are congruent, we can use the concept of parallel lines and alternate interior angles.

Explanation

"Congruent" is a term used in geometry to describe objects that have the same size and shape. In other words, if you can transform one object into the other by translation (sliding), rotation, and possibly reflection (flipping), then the two objects are considered congruent.

For example:

Two triangles are congruent if their corresponding sides are of equal length, and their corresponding angles are equal.

Two circles are congruent if they have the same radius.

Two rectangles are congruent if they have the same length and width.

The term "congruent" is often denoted by the symbol ≅. So, if two triangles are congruent, you could write it as Triangle ABC ≅ Triangle DEF.

Congruence is an important concept in geometry and is used to establish relationships between different geometric figures based on their sizes and shapes.

To prove that the corresponding angles EBI and BCJ are congruent, we can use the concept of parallel lines and alternate interior angles. We are given that JLines AI and GJ are parallel, and we want to show that EBI and BCJ are congruent.

Since AI and GJ are parallel, angle EBI and angle BCJ are alternate interior angles. According to the theorem, if two parallel lines are intersected by a transversal, then the alternate interior angles are congruent.

Therefore, the correct answer is A) Translation, as it is the transformation that preserves the angle measure and maintains the congruence of the corresponding angles.

Answer 2

Reflecting the figure over a line perpendicular to the parallel lines AI and GJ would prove that the corresponding angles EBI and BCJ are congruent.

Step-by-step explanation:

The question involves finding the transformation that would prove that the corresponding angles EBI and BCJ are congruent, given that lines AI and GJ are parallel. Reflecting the entire figure over the line that is perpendicular to AI and GJ at the point where EBI intersects this line would map angle EBI onto angle BCJ. Since reflections preserve angle measure and a reflection over a perpendicular bisector maps one figure onto another with corresponding parts congruent, this transformation demonstrates the two angles, EBI and BCJ, are congruent.