Similar, Then Find

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 54 of 60.

Once two triangles are similar, their matching sides are in one ratio, so one known pair gives the others. The rule Similar triangles finds a side, and the board checks that the triangles really are similar: here AA from the parallel lines.

$Triangle ABC with DE parallel to BC; AD = 2, DB = 6, BC = 20, DE unknown$

The big triangle's side AB is $2+6 = 8$ , four times AD, so every side of △ABC is four times the matching side of △ADE. DE matches BC, so DE is 20 ÷ 4 = 5. The trap is using DB instead of AB: DB is not a side of the small triangle, and it does not match AD.

Challenge

In △PQR the segment ST is parallel to QR. PS = 3, SQ = 6 and QR = 12. Find ST, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same Shape What Congruence Gives Recap: Matching Parts

5ASA and AAS

The Side Between The ASA Rule The AAS Rule ASA or AAS?Recap: ASA and AAS

8Proofs with Vertical Angles

Vertical Angles in Proofs The Bowtie Bowtie with ASA Linear Pairs in Proofs Recap: Vertical Angles

11Similarity Proofs