Back to Prove theorems using similarity — Problem 5 · 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.

$Right triangle with altitude CD to hypotenuse. AD = 3, DB = 12, CD = h = ?.$

In right $\triangle ABC$ with right angle at $C$ , altitude $\overline{CD}$ meets
hypotenuse $\overline{AB}$ at $D$ with $AD = 3$ and $DB = 12$ .
Using $\triangle ACD \sim \triangle CBD$ , find the altitude length $CD$ .