Remember that the hypotenuse of a right triangle must be the longest side. Use the Isosceles Triangle Theorem to obtain a pair of congruent angles.
Practice makes perfect
We need to draw an isosceles triangle △ ABC with m∠B=90^(∘). This means that △ ABC is a right triangle. From this information, we can say that the congruent sides are the legs of △ ABC, since the hypotenuse has to be the longest side.
We have that AB ≅ BC. By applying the Isosceles Triangle Theorem, we get that ∠A ≅ ∠C.
From the above, we have that m∠A=m∠C. Since the sum of the measures of the interior angles of a triangle must add to 180^(∘), we get the following equation.
m∠A+ m∠B + m∠C &= 180^(∘)
Next let's substitute m∠B=90^(∘) and m∠A=m∠C, and solve the resulting equation for m∠A.
