Q10 If ED炉AC炉, name all pairs of a... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 3: Q10 (page 89)

If $\overset{炉}{E D}|| \overset{炉}{A C}$ , name all pairs of angles that must be congruent.

Short Answer

Expert verified

The required pairs are $鈭� 8 鈮� 鈭� 2$ and $鈭� 4 鈮� 鈭� 7$ .

Step by step solution

Step 1. Determine the theorem or postulate that can be used

Postulate 10 states when a separate line travels through two lines which are having a parallel relation between them at that time the angles which are corresponding angles represents the congruent angles.

Theorem 3-2 states when a separate line travels through two lines which are having a parallel relation between them at that time the angles which are positioned on alternate interior side represents the congruent angles.

Step 2. Determine the angles that are congruent

The angles $鈭� 8$ and $鈭� 2$ are positioned on the transversal $\overset{炉}{E B}$ but these angles are having the opposite sides along with this these angles are representing the non adjacent interior angles. So according to the definition of alternate interior angles which states that angles are alternate interior angles when they are positioned on the transversal but these angles are having the opposite sides along with this these angles are representing the non adjacent interior angles the angles are alternate interior angles.

The angles $鈭� 7$ and $鈭� 4$ are having the same properties like $鈭� 8$ and $鈭� 2$ but the transversal is $\overset{炉}{D B}$ so the angles are alternate interior angles.