a By the Corresponding Angles Theorem, you know that two sides are parallel.
B
b By the Corresponding Angles Converse, you know that corresponding angles are congruent.
A
a See solution
B
b See solution
Practice makes perfect
a According to the Corresponding Angles Theorem, if two parallel lines are cut by a transversal, then the pair of corresponding angles are congruent. Let's illustrate this.
We want to show that
∠ 1 ≅ ∠ 2
using translations. AB and CD are parallel segments, we can view them as translations of each other. In other words, we can actually move one so that it covers the other
Because a translation is a rigid motion, and a rigid motion preserves length and angle measures, we know that the angle that AB creates with the transversal, will be preserved when it's translated to CD. Therefore, we can say that
∠ 1≅ ∠ 2
b According to the Corresponding Angles Converse, if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel. Here we can use the same reasoning as in the previous question. Let's draw the diagram.
We want to show that
AB ∥ CD
using translations. If we translate B until it reaches the same intersection point with the transversal as CD, then the marked angle of the image will be congruent with it's preimage.
Since the two lines create the same angle with the transversal, they overlap and are parallel.
