SME
Grade 10 Math · Problem type
Base angles of an isosceles triangle
Use this for “Given AB = AC, prove ∠B = ∠C” and “An isosceles triangle has a 40° vertex angle. What are its base angles?”
Diagram
Step 1 of 5: AB = AC (given).
Yellow: what the step uses.
Blue: what it proves.
This is an example. Type your own values to start a new problem.
B
°
=
180°
−
°
2
s
Legs AB = AC
example
k
Proof step
example
Formulas
B
=
180 −
A
2
70
=
180 − 40
2
Assumptions
•
Given: AB = AC. Draw AD, the bisector of ∠A, to meet BC at D.
•
Step through the proof: each step lights what it uses and what it proves.
•
The base angles are equal, so each is half of what is left of 180°.
Step-by-step
WE KNOW
s = 6 cm, A = 40°, k = 1
FIND
base angle B (B)
Step 1 · Find base angle B (B)
Use B = (180 − A) ÷ 2
The two base angles are equal and share what is left of 180°.
B
=
180 − 40
2
B
=
140
2
B
=
70°
Check
Put the numbers back in. Both sides should match.
70
=
180 − 40
2
✓
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Triangle angle sum and exterior angle
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Conditional, converse, inverse, contrapositive
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