Cogito
Geometry · Chapter 4 · Lesson 1
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
What this lesson teaches
The student proves triangles similar by AA and uses proportions to find missing lengths.
- Two matching angles prove triangles similar.
- Corresponding sides are then in one ratio.
- A line parallel to a side splits the other two proportionally.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Isosceles and Equilateral Triangles: Base angles 55°. Apex, in degrees?
Answer 70
Why 70°.
Review — Writing a Two-Column Proof: Is "given" a valid reason for a first line? 1 for yes, 0 for no.
Answer 1
Why Yes.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSimilar. 8 matches 20, another side is 6. Its match?
Answer 15
Why 15.
Why do two matching angles prove similarity?
Answer The third angle is then forced to match.
Why The angle sum forces the third.
Similar. 5 matches 15, another side is 4. Its match?
Answer 12
Why Factor 3.
Similar. 6 matches 9, another side is 8. Its match?
Answer 12
Why Factor 1.5.
Build It Up
The same ideas with more to keep track of.
2 problemsTwo triangles share angles of 40° and 65°. Are they similar?
Answer Yes, by AA.
Why Two angles is enough.
Similar triangles, one angle is 55°. The matching angle?
Answer 55
Why Angles are preserved.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Shadow: A 3 m post casts a 4 m shadow. A tree casts a 20 m shadow. How tall is the tree?
Answer 15 m
Why 15 m.
The Proportion: Similar triangles. 4 matches 10, and another side is 6. Its match?
Answer 15
Why 15.