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Q5

Expert-verifiedFound in: Page 45

Book edition
Student Edition

Author(s)
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages
227 pages

ISBN
9780395977279

State which postulate, definition, or theorem justifies the statement about the diagram.

If *E* is the midpoint of $\overline{AF}$, then $AE=\frac{1}{2}AF$.

The fact that the **midpoint of a line divides it into equal parts** justifies the statement about the diagram.

The diagram constitutes a straight-line *AEF* and two other lines meet the line *AEF* at the point *E*. *E* is the midpoint of *AF*.

The theorem states that if *E* is the midpoint of *AF*, then *AE* is equal to *EF*.

As *E* is the midpoint of *AF*,

Then, $AE=EF$.

Also,

$\begin{array}{c}AE+EF=AF\\ AE+AE=AF\end{array}$

$2AE=AF$

$AE=\frac{1}{2}AF$

Hence, the statement is proved if the midpoint of a line divides it into equal parts.

Therefore, the statement about the diagram is justified by the reason that the midpoint of a line divides it into equal parts.

Prove the following statement by filling in the blanks.

If *A* and *B* have coordinated *a* and *b*, with $b>a$, and the midpoint *M* of $\overline{AB}$ has coordinate *x*, then prove $x=\frac{a+b}{2}$.

Proof:

Statement | Reasons |

1. | 1. ? |

2. $AM=x-a\text{};\text{}MB=b-x$ | 2. ? |

3. | 3. ? |

4. $\overline{AM}\cong \overline{MB}$, or $AM=MB$ | 4. ? |

5. $x-a=b-x$ | 5. ? |

6. $2x=$? | 6. ? |

7. $x=\frac{a+b}{2}$ | 7. ? |

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