Cogito
Geometry · Chapter 3 · Lesson 3
Isosceles and Equilateral Triangles
Equal sides force equal angles.
11 problems · about 22 minutes · G-CO.C.10
What this lesson teaches
The student uses the base angle theorem and its converse.
- Equal sides force the angles opposite them to be equal.
- The converse holds too: equal angles force equal sides.
- An equilateral triangle therefore has three 60° angles.
Warm Up
Straightforward practice. Get the method working first.
4 problemsBase angles 55°. Apex, in degrees?
Answer 70
Why 70°.
Base angles 50°. Apex, in degrees?
Answer 80
Why 180 − 100.
Apex 40°. One base angle, in degrees?
Answer 70
Why 140 ÷ 2.
Two angles are 45° and 45°. Is it isosceles? 1 for yes, 0 for no.
Answer 1
Why The converse.
Build It Up
The same ideas with more to keep track of.
3 problemsApex 90°, isosceles. One base angle, in degrees?
Answer 45
Why 90 ÷ 2.
How many equal sides does an equilateral triangle have?
Answer 3
Why All of them.
Sort each triangle by how many equal sides it has.
Answer Three equal: Equilateral · Exactly two equal: Isosceles · No equal sides: Scalene
Why Scalene is the one with nothing equal.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsBase angles 30°. Apex, in degrees?
Answer 120
Why 180 − 60.
Is every equilateral triangle also isosceles? 1 for yes, 0 for no.
Answer 1
Why It has at least two equal sides.
The Apex: Base angles 70°. What is the apex, in degrees?
Answer 40
Why 40°.
Equilateral: One angle of an equilateral triangle, in degrees?
Answer 60
Why 60°.