Becoming a ‘Geometry Lawyer’. Lesson 1. Similar Triangles. Last week we learned what similar triangles are, and how we can use them to find side lengths. What is the minimum amount of information you need to know to declare two triangles SIMILAR?
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Pretend you are a lawyer. Your job is to convince a Geometry judge that these two triangles are similar.
First, you need to know what to show the judge! We just saw that AA will be enough to convince the judge, since if two corresponding angles are congruent, then the triangles are similar.
SO, show that two corresponding angles ARE congruent.
∠PRQ is congruent to ∠SRT by VA. (There is one set of congruent angles)
It is given that PQ and ST are parallel, therefore,
∠QPR is congruent to ∠RTS by AIA (The second set of congruent angles)
Thus, ∆PQR ~ ∆TSR! □
By SAS, ∆ABC is congruent to ∆XYZ