Explain how and why Euclid’s proof of his Proposition 15 works.

Question

Euclid's proposition 15 is:

15) Vertically opposite angles are equal.

Answer 1

4 angles at the junction A ,B,c,d clockwise.

A and C are vertically opposite, as are B and D.

A÷B=180 as they are linear pair.

B+C=180 as they are linear pair.

Then A+B=B+C by substitution/transitive.

Therefore A=C upon subtracting B from both sides.

You can repeat the same argument to show B=D

Which is left for you as an exercise. You also need to draw the picture