a In a triangle, the size of an angle relative to the other angles depends on the length of that angle's opposite side. A side that is relatively smaller makes for a smaller angle, and vice-versa.
Since a
In an equilateral triangle all three sides have the same length, which means the measure of each angle must be the same. That is, if a=b=c then it must be that A=B=C as well.
b As explained in Part A, the opposite angles to two congruent sides of a triangle are congruent. With this information, we know that the unknown angles of the isosceles right triangle have the same measure.
Using the Triangle Angle Sum Theorem, we can set up an equation.
θ+θ+90^(∘)=180^(∘)
Let's solve this equation for θ.
The remaining two angles are both 73^(∘). As discussed in Part A, the side opposite the smallest angle is the shortest side. Also, if two angles have the same measure, the sides opposite of these angles have the same length. Therefore, BC is the shortest while AB and AC is the longest.
