Question

In the diagram below, EF intersects AB and CD at G and H.respectively. Gl is kn drawn such that GH BIH.If mxE6B = 50 and m&DIG = 115, explain why AB CD. [4 pts)

Answer 1

The line AB is parallel to CD because of the corresponding angle theorem.

Corresponding angle theorem;

The corresponding angle theorem states that suppose we have two parallel lines AB and CD, and these two parallel lines has a transversal line that cuts through both parallel lines, then the pairs of the corresponding angles are similar angles. This notion tells us that AB and CD are parallel lines.

From the given information,

• ∠EGB is corresponding to ∠GHI = 50°
• ∠BGH is corresponding to ∠DHF = 130°

Therefore, the corresponding angle theorem states that if we can prove that one pair of angle in line AB is a corresponding angle to line CD, then the angles are similar or congruent, and line AB is parallel to line CD.

Answer 2

We are given the following information

Line EF intersects line AB and line CD

GH ≅ IH

m∠EGB = 50° and m∠DIG = 115°

We are asked to explain that why line AB is parallel is line CD.

As you can see, corresponding angles are equal so, m∠GHI = m∠EGB = 50°

We know that angles on a straight line equal 180°

`m\angle GIH=180-115=65\degree`

Therefore, in triangle GHI, angle H equals 50, angle I equals 65 and angle G equals 65

Angles in a triangle equals 180

Therefore, lines AB and CD are parallel