Step 1: Find the length of .
Use Pythagoras' theorem, which states that the square of the length of a right-angled triangle's hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Substitute the known lengths in , and solve for the length of .
Step 2: Find the length of .
Since is the midpoint of ,
and are vertical angles, so they are equal in measure.
Two right-angled triangles are congruent if the leg and an acute triangle of one triangle are congruent to the corresponding parts of the other triangle. Since and , is congruent to .
The corresponding sides of congruent triangles are equal in length. Therefore,