It is given that segment AB is parallel to segment CD and points E, G, H, and F are collinear. by the Vertical Angles Theorem. ∠AGF and ∠CHF are corresponding and congruent according to the Corresponding Angles Theorem. Finally, ∠EGB and ∠CHF are congruent by the .

∠EGB and ∠AGF are congruent; Transitive Property of Equality

Step-by-step explanation:

The vertical angles theorem refers to the angles which are opposite to each other also it created two lines that are intersected each other

Here congruent refers that their measures are equivalent to each other

As mentioned that

AB || CD

E, G, H, F are col-linear

Also, the points E, G, H, F is transversal for the parallel lines

Since AB and EF intersected at G point

Therefore

m∠EGB = m∠AGF

By applying the verticles angle theorem

As AB and EF intersected at G point so they create opposite angles i.e EGB and AGF

Therefore

m∠AGF = m∠CHF

By applying the corresponding angles theorem

Now

The Transitive Property of Equality refers that if one angle is equivalent to two angles then these two angles are equal  l

Like

a = b and b = c,

So, a = c

Like

m∠EGB = m∠AGF

m∠AGF = m∠CHF

So, ultimately

m∠EGB = m∠CHF are congruent

no

step-by-step explanation:

the answer would be 0.54