Will give brainliest for Two-column or paragraph proof!

In the figure below, ∠DEC ≅ ∠DCE, ∠B ≅ ∠F, and segment DF is congruent to segment BD. Point C is the point of intersection between segment AG and segment BD, while point E is the point of intersection between segment AG and segment DF.

Prove Triangle ABC is congruent to Triangle GFE

Step-by-step explanation:

Angle B and angle F are known to be equal.

Since angles DCE and DEC are equal, angles ACB and GEF are also equal (vertically opposite angles)

When two angles are equal, the third angle has to be equal too because total angle of both triangles is the same, i.e 180

Now when angles are equal, if we just show that lengths BC ans EF are also equal, it would be sufficient to say that the two triangles are congruent.

Since triangle DCE is an isosceles triangle (because two angles same),

Length CD = ED

We know that

Length of BD = Length FD

Length CD = Length ED

Length of BC = BD - CD

Length of EF = FD - ED

Therefore,

Length BC = Length EF

When all angles are equal, and even one pair of corresponding lengths is equal.. the triangles are congruent

x = 25

step-by-step explanation:

a^2+b^2=c^2

7^2+24^2=c^2

49+576=625

sqrt625=25

x=25