Cogito
Geometry · Chapter 5 · Lesson 3
Special Right Triangles
Two triangles worth knowing by heart.
11 problems · about 22 minutes · G-SRT.C.6
What this lesson teaches
The student uses the 45-45-90 and 30-60-90 side ratios.
- A 45-45-90 triangle has sides in ratio 1 : 1 : √2.
- A 30-60-90 has sides 1 : √3 : 2, and the shortest side is half the hypotenuse.
- Both come from cutting a familiar shape in half.
Warm Up
Straightforward practice. Get the method working first.
4 problems30-60-90 with hypotenuse 18. Shortest side?
Answer 9
Why 9.
30-60-90 with hypotenuse 20. Shortest side?
Answer 10
Why Half.
30-60-90 with shortest side 7. Hypotenuse?
Answer 14
Why Double.
45-45-90 with legs 6. What is the hypotenuse squared?
Answer 72
Why 36 + 36.
Build It Up
The same ideas with more to keep track of.
3 problemsIn a 45-45-90, are the two legs equal? 1 for yes, 0 for no.
Answer 1
Why Two equal angles.
Match each triangle to its side ratio.
Answer 45-45-90 → 1 : 1 : √2; 30-60-90 → 1 : √3 : 2
Why The one with equal legs has two matching numbers.
Which angle faces the shortest side in a 30-60-90? Give the degrees.
Answer 30
Why The smallest angle.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsA 45-45-90 is half of which shape? 1 for square, 2 for equilateral triangle.
Answer 1
Why Cut along a diagonal.
30-60-90 with hypotenuse 30. Shortest side?
Answer 15
Why Half.
Half the Hypotenuse: A 30-60-90 with hypotenuse 12. What is the shortest side?
Answer 6
Why 6.
The Square: A 45-45-90 with legs 1. What is the hypotenuse squared?
Answer 2
Why 2.