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This guide presents a multi-step problem involving the distances between stores in a shopping mall. It illustrates the relationships between the entrances of a food court, music store, shoe store, and bookstore, establishing a crucial mathematical proof using midpoints. By visualizing these relationships with clear diagrams and applying the Transitive Property of Congruence, readers can understand the proof process. This resource is tailored for students looking to enhance their problem-solving skills in geometry.
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Shopping Mall EXAMPLE 4 Solve a multi-step problem 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.
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.
GIVEN: Bis the midpoint of AC. Cis the midpoint of BD. 4. Transitive Property of Congruence 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 ABCD 4. 5. AB = CD 5. Definition of congruent segments EXAMPLE 4 Solve a multi-step problem
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?
