Prove triangle theorems including angle sum, isosceles base angles, midsegment theorem, and medians concurrence.
Complete a structured triangle-theorem reasoning chain
Problem
In triangle \(ABC\), \(AB~=~AC\) and \(m\angle~A~=~40°\). Use the isosceles triangle theorem to relate \(\angle~B\) and \(\angle~C\), write the triangle angle-sum equation, and calculate \(\text{both}~\text{base}-\angle~\text{measures}\).
Two theorems work in sequence: the side marks first make the base angles equal, and the triangle total then determines their common measure. We’ll represent both with one variable, subtract the known vertex angle from the full total, divide the remainder evenly, and check all three angles.
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