Shopping Mall
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EXAMPLE 4

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Example 4

Shopping Mall

Walking down a hallway at the mall, you notice the music store is halfway between the food court and the shoe store. The shoe store is halfway between the music store and the bookstore. Prove that the distance between the entrances of the food court and music store is the same as the distance between the entrances of the shoe store and bookstore.

EXAMPLE 4

Solve a multi-step problem


Example 4

Draw and label a diagram.

Draw separate diagrams to show mathematical relationships.

EXAMPLE 4

Solve a multi-step problem

SOLUTION

STEP 1

STEP 2

State what is given and what is to be proved for the situation.

STEP 3

Then write a proof.


Example 4

GIVEN:

Bis the midpoint of AC.

Cis the midpoint of BD.

PROVE:

AB = CD

REASONS

STATEMENT

1.

1.

Bis the midpoint of AC.

Given

Cis the midpoint of BD.

ABBC

2.

2.

Definition of midpoint

3.

3.

BCCD

Definition of midpoint

EXAMPLE 4

Solve a multi-step problem


Example 4

4.

Transitive Property of Congruence

ABCD

4.

5.

AB = CD

5.

Definition of congruent segments

EXAMPLE 4

Solve a multi-step problem


Example 4

ANSWER

No; Because the critical factor is the midpoint

ANSWER

Food Court and Bookstore

for Example 4

GUIDED PRACTICE

5. In Example 4, does it matter what the actual distances are in order to prove the relationship between ABand CD? Explain.

6. In Example 4, there is a clothing store halfway between the music store and the shoe store. What other two store entrances are the same distance from the entrance of the clothing store?


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