Back to Prove theorems using similarity — Problem 3 · Task Set 17

Exercises: Prove Theorems Using Similarity

Show all work. For proof problems, write complete reasoning in paragraph or two-column form.

Grade 9·21 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-srt-b-4

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Fluency Practice

Apply the Side-Splitter Theorem, its converse, or right-triangle similarity to find unknown values.

$Triangle ABC with segment DE. AD = 8, DB = 4, AE = 10, EC = 5. Is DE parallel to BC?$

In $\triangle ABC$ , point $D$ lies on $\overline{AB}$ and point $E$ lies on $\overline{AC}$ .
Given $AD = 8$ , $DB = 4$ , $AE = 10$ , and $EC = 5$ . Is $DE \parallel BC$ ?

Yes — the ratios $AD/DB$ and $AE/EC$ are equal, so by the converse of the Side-Splitter Theorem, $DE \parallel BC$ .

No — the ratios are not equal, so $DE$ is not parallel to $BC$ .

Yes — $DE$ divides two sides of the triangle, so it must always be parallel to the third side.

Cannot be determined without knowing the lengths of $DE$ and $BC$ .