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Cogito

Geometry · Chapter 4 · Lesson 1

Practice Worksheet

Similar Triangles and AA

Two angles are enough.

10 problems · about 20 minutes · G-SRT.A.2, G-SRT.A.3, G-SRT.B.5

NameDate

Figure — use these to answer the problems

Matching sides of similar triangles share one ratio.
A ratio table for 3 to 9
Small triangleLarge triangle
39
618
Small triangleLarge triangle0039618
Side on the small one3
Matching side on the large one9
Scale it up by2
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Isosceles and Equilateral Triangles”

    Base angles 55°. Apex, in degrees?

    Answer

  2. From “Writing a Two-Column Proof”

    Is "given" a valid reason for a first line? 1 for yes, 0 for no.

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Similar. 8 matches 20, another side is 6. Its match?

    Answer

  2. Why do two matching angles prove similarity?

    • The third angle is then forced to match.
    • Because that is the rule.

  3. Similar. 5 matches 15, another side is 4. Its match?

    Answer

  4. Similar. 6 matches 9, another side is 8. Its match?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Two triangles share angles of 40° and 65°. Are they similar?

    • Yes, by AA.
    • No.

  2. Similar triangles, one angle is 55°. The matching angle?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Shadow

    A 3 m post casts a 4 m shadow. A tree casts a 20 m shadow. How tall is the tree?

    Answerm

  2. The Proportion

    Similar triangles. 4 matches 10, and another side is 6. Its match?

    Answer