Geometry question

Question

Prove ade is congruent to bde if acd is congruent to bcd

Answer 1

I am going to presume that points abcde are collinear.

We are given that line segment bcd is congruent to acd (in other words, their lengths are the same).

Every geometric object is congruent to itself by the reflexive property of congruence, so de = de.

By the line segment addition postulate,

acde = acd + de

and

bcde = bcd + de

But acde is the same line segment as ade, and bcde is the same line segment as bde.

So,

ade = acd + de

and

bde = bcd + de

Subtracting de (the length of line segment de) from the left and right sides of this equation, we arrive at

ade = bde

QED

(I'm sure you can put this into two-column format if you need to. Let me know if you need help with this.)