Back to Prove theorems using similarity — Problem 4 · 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.

$Right triangle ABC with altitude CD to hypotenuse AB. AD = 4, DB = 9, AC = ?.$

Right triangle $\triangle ABC$ has a right angle at $C$ . The altitude from $C$ meets
hypotenuse $\overline{AB}$ at point $D$ , with $AD = 4$ and $DB = 9$ .
Using the similarity of $\triangle ACD$ and $\triangle ABC$ , find $AC$ .