CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal. ∠GAC ≅ ∠HFD by the transitive Property of Congruence.
What are congruent angles?
Angles that are of the same measurement are called congruent.
Suppose that two angles ∠A and ∠B are of the same measure,
then
[tex]m\angle A = m\angle B[/tex]
is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.
We write the congruency between them as;
[tex]\angle A \cong \angle B[/tex]
In the figure BC || DE .
Angles
CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal.
GAC and DFE are not congruent
CAF and EFH are not congruent
GAB and EFA are not congruent
∠GAC ≅ ∠AFE because they are corresponding angles of parallel lines cut by a transversal.
∠AFE ≅ ∠HFD by the Vertical Angles Theorem.
Therefore, ∠GAC ≅ ∠HFD by the transitive Property of Congruence.
∠AFD = ∠AFE
Two angles that are equal to the same angle must themselves be equal.
( By Transitive property of equality)
Learn more about congruent angles;
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