Back to Prove theorems using similarity — Problem 2 · 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.

$Triangle PQR with parallel segment ST. PS = 5, SQ = 3, PT = 7.5, TR = ?.$

In $\triangle PQR$ , segment $ST \parallel QR$ with $S$ on $\overline{PQ}$ and $T$ on $\overline{PR}$ .
Given $PS = 5$ , $SQ = 3$ , and $PT = 7.5$ , find $TR$ .