Question

Copyright by fidougal Littell, a division

12. Bleycle Tour You take part in a three day bicycle tour. On the first day, you ride
95 miles. On the third (final) day, you also ride 95 miles. Use the following steps to
prove that the distance you ride in the first two days is equal to the distance that you
ride in the last two days.


a. Draw a diagram for the situation by using a line segment to represent the total distance of the three days and dividing the line segment into three parts that represent the daily distances.

b. State what is given and what is to be proved.

c. Write a two-column proof.
Statements


Given: AB = 95
CD=95
Prove AB+ BC = BC+CD

Answer 1

Given: AB = 95 miles (distance on the first day)

CD = 95 miles (distance on the third day)

To be proved: AB + BC = BC + CD

Statements:

• AB = 95 (Given)

• CD = 95 (Given)

• AB + BC = BC + CD (To be proved, as it is the statement to be shown equal)

• BC + AB = BC + CD (Communitive property of addition, from statement 3)

• AB + BC = CD + BC (Communitive property of addition, from statement 4)

• AB + BC = BC + CD (Transitive property of equality, from statements 3 and 5)

Hence, AB + BC is equal to BC + CD as proven in the two-column proof.