Chapter 4.2, Problem 43E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Prove that the segment that joins the midpoints of two sides of a triangle has a length equal to one-half the length of the third side.

*(HINT: In the drawing,*
*is extended to*
*, a point on*
*. Also,*
*is a parallel to*
*.)*

To determine

**To prove:**

The segment that joins the midpoints of two sides of a triangle has a length equal to one-half the length of the third side.

Explanation

Formal proof:

Statement:

The segment that joins the midpoints of two sides of a triangle has a length equal to one-half the length of the third side.

Drawing:

Given:

Prove:

PROOF | |

Statement | Reasons |

1. |
1. Given |

2. Produce |
2. Construct a parallelogram |

3 |

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