Question

How on earth do you do this. Proofs are hard how are people even good at these. ​

Answer 1

Answer:

see below

Step-by-step explanation:

Hi there!

We're given the triangle ABC with lines AC and BC extended to get the lines AD and BE.

<DEC is formed by lines AD and BE, with C as the vertex.

We're also given that <4≅<5.

You may notice that <DCE and <5 are vertical angles, which means that they share the same vertex (vertex C), and are opposite to each other.

There is a theorem that states vertical angles are congruent.

therefore, <DCE≅<5 by vertical angle's theorem.

But we need to prove that <DCE≅<4

There is a property known as transitivity, where if a=b and b=c, then a=c.

Since both <DCE and <4 are congruent to <5, they also must be congruent to each other via transitivity

Hope this helps! :)

Answer 2

Answer:

Angle DCE is congruent to angle 5 because they are vertical angles. If angle 4 is congruent to angle 5, that means it is also congruent to angle DCE by the transitive property.

Step-by-step explanation: