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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 ∠2≅∠3then AD||BC.

Short Answer

Expert verified

Theorem 3 – 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∠2and∠3are the alternate interior angles which are formed when the lines AD↔ andBC↔are cut by the transversal DB↔ .

02

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

Theorem 3 – 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 ∠2≅∠3, so by the theorem 3 – 5, it can be said that the lines AD↔ andBC↔are parallel.

That is, AD↔||BC↔.

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Most popular questions from this chapter

Classify each pair of angles as alternate interior, same side interior or corresponding angles

and

State the postulate or theorem that justifies each statement.

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Exercises 23-29 refer to the diagram in step 2 of exercise 22.

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Exercises 23 – 29 refer to the diagram in Step 2 of Exercise 22

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State the postulate or theorem that justifies each statement.

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