Cogito
Grade 7 Math · Chapter 8 · Lesson 4
When Three Measurements Fix a Triangle
One triangle, many, or none at all.
10 problems · about 19 minutes · 7.G.A.2
What this lesson teaches
The child decides whether given conditions determine a unique triangle, more than one, or none.
- Three sides that satisfy the triangle inequality give exactly one triangle.
- Three angles give infinitely many, all the same shape at different sizes.
- Any two sides added must beat the third, or nothing closes.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Angle Pairs: Supplement of 130°?
Answer 50
Why 50°.
Review — Volume and Surface Area of Prisms: Base area 18, height 7. Volume?
Answer 126
Why 126.
Review — Angle Pairs: Supplementary to 47?
Answer 133
Why 133 degrees.
Warm Up
Straightforward practice. Get the method working first.
3 problemsCan sides 4, 4 and 9 make a triangle? 1 for yes, 0 for no.
Answer 0
Why No — 8 is less than 9.
Angles 30° and 90°. What is the third?
Answer 60
Why 180 − 120.
Can sides 5, 6 and 10 make a triangle? 1 for yes, 0 for no.
Answer 1
Why 5 + 6 against 10.
Build It Up
The same ideas with more to keep track of.
2 problemsCan sides 1, 2 and 8 make a triangle? 1 for yes, 0 for no.
Answer 0
Why 1 + 2 against 8.
Do three given angles fix the size of a triangle? 1 for yes, 0 for no.
Answer 0
Why They fix the shape only.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Third Angle: A triangle has angles of 50° and 60°. What is the third, in degrees?
Answer 70
Why 70°.
The Impossible Triangle: Can sides 2, 3 and 9 make a triangle? Answer 1 for yes, 0 for no.
Answer 0
Why No.