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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
4. Parallel Lines and Proportional Parts
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Exercise 50 Page 580

Use the definition of midpoint and the Triangle Midsegment Theorem.

Statements
Reasons
1.
AB=4, BC=4, and CD=DE
1.
Given
2.
AB=BC
2.
Transitive Property of Equality
3.
B is the midpoint of AC
D is the midpoint of CE
3.
Definition of midpoint
4.
BD∥ AE
4.
Triangle Midsegment Theorem
Practice makes perfect

We are given the diagram below in which AB=4, BC=4, and CD=DE.

By the Transitive Property of Equality, AB=BC. Then, according to the definition of congruent segments we have that AB≅BC and CD≅DE

In consequence, B and D are the midpoints of AC and CE.

The Triangle Midsegment Theorem gives us that BD∥ AE.

Two-Column Proof

Given: & AB=4,BC=4,and CD=DE Prove: & BD∥ AE Let's summarize the proof we did above in the following two-column table.

Statements
Reasons
1.
AB=4, BC=4, and CD=DE
1.
Given
2.
AB=BC
2.
Transitive Property of Equality
3.
B is the midpoint of AC
D is the midpoint of CE
3.
Definition of midpoint
4.
BD∥ AE
4.
Triangle Midsegment Theorem
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