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Chapter 3: Q30. (page 115)

Name or state the postulate, definition, or theorem that justifies each statement about the diagram.

If 鈭�2鈮�鈭�3then AD||BC.

Short Answer

Expert verified

Theorem 3 鈥� 5 is used to justify the above statement.

Step by step solution

01

Step 1. Observe that angle ∠2 and ∠3 are alternate interior angles.

From the figure, it can be observed that the angles鈭�2and鈭�3are the alternate interior angles which are formed when the lines AD鈫� andBC鈫�are cut by the transversal DB鈫� .

02

Step 2. Determine the theorem or postulate that can be used.

Theorem 3 鈥� 5 states that if two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

03

Step 3. Apply the theorem.

Since 鈭�2鈮�鈭�3, so by the theorem 3 鈥� 5, it can be said that the lines AD鈫� andBC鈫�are parallel.

That is, AD鈫�||BC鈫�.

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