Geometry: An Interactive Journey to Mastery

Lesson 10: Practical Applications of Similarity

Study Tip

x Triangles are the “atoms” of geometry, and identifying similar triangles in complicated diagrams

is often the key to unlocking results about that diagram. Become familiar with all three similarity

principles for triangles: SAS, AA, and SSS.

Pitfall

x For the SAS principle, the angle in consideration must

be sandwiched between the two sides in consideration.

For example, in the diagram in Figure 10.7, triangles

PQS and PQR both share the angle A and have two

matching sides of lengths 10 and 3, yet they are clearly

QRWVLPLODUWULDQJOHVͼ௘7KHDQJOHA is not sandwiched

EHWZHHQWKHVLGHVRIOHQJWKVDQG௘ͽ

1. Each of the following pictures shows a pair of triangles. Which pairs of triangles are certain to be similar?
   Which are certain to be congruent? Of those that are similar/congruent, explain which principle gives
   you this.
   D௘ͽ
   3 a
   3 b

b

a

Figure 10.8

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Figure 10.9

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xxh

Figure 10.10

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Figure 10.11

PRA S

Q

(^1033)
Figure 10.7
Problems