Please help me with the following question I dont want an ol

Please help me with the following question. I don\'t want an old answer which is already posted on chegg. If you write it by hand, make sure it is clear to read.

Prove Proposition 4.2. (Hint: See Figure 4.6. On the ray opposite to AC, lay off segment AD congruent to A\'C\'. First prove DAB AC A B\'; then use isosceles triangles and a congruence criterion to conclude.)

Solution

Given that Angle BAC = Angle B\'A\'C\' =90. So they are both right angle triangles. Also given that their hypotenuse is equal i.e BC=B\'C\'

Let us assume one leg of each traingle BA=B\'A\'. then by pythagoras theorem, we have that AC² = BC²-AB² and

A\'C\'2 = B\'C\'²-A\'B\'² and since BC=B\'C\' and BA=B\'A\', therefore AC=A\'C\'.

Hence all three sides are equal and the 2 triangles are congruent.