Question 7 (Multiple Choice Worth 5 points) (03.05 MC) Theorem: A line parallel to one side of a triangle divides the other two proportionately. In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB: A 6 12 D E 18 B F 24 C Which statement can be proved true using the given theorem? Segment BD = 12 Segment BD = 4 Segment BF = 16 Segment BF = 9
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Theorem: A line parallel to one side of a triangle divides the other two proportionately. In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB: Which statement can be proved true using the given theorem? Segment BD = 32 Segment BD = 36 Segment BF = 15 Segment BF = 18
James K.
Sri K.
Complete the paragraph proof of Theorem $6-2-4$ by filling in the blanks. Given: $A B C D$ is a parallelogram. Prove: $\overline{A C}$ and $\overline{B D}$ bisect each other at $E$ Proof: It is given that $A B C D$ is a parallelogram. By the definition of a parallelogram, $\overline{A B} \|$ a. $\quad$ ? $\quad$ By the Alternate Interior Angles Theorem, $\angle 1 \cong$ b. $\quad ?$, and $\angle 3 \cong \mathrm{c}, \quad ? \quad \overrightarrow{A B} \cong \overline{C D}$ because $\mathrm{d} . \quad ? \quad .$ This means that $\triangle A B \bar{E} \cong \triangle C D E$ by e. $\quad ? \quad .$ So by $\mathbf{f} . \quad ?, \overline{A E} \cong \overline{C E},$ and $\overline{B E} \cong \overline{D E} .$ Therefore $\overline{A C}$ and $\overline{B D}$ bisect each other at $E$ by the definition of $\mathbf{g} .$ (GRAPH CANT COPY)
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