Answer:
The two triangles are similar by AAA
Step-by-step explanation:
we know that
If the two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent
Remember that
The sum of the internal angles of a triangle must be equal to [tex]180\°[/tex]
so
In the triangle CDE
Find the measure of angle E
[tex]m<C+m<D+m<E=180\°[/tex]
substitute the values and solve for m<E
[tex]60\°+53\°+m<E=180\°[/tex]
[tex]m<E=180\°-(60\°+53\°)=67\°[/tex]
The measures of internal angles triangle CDE are [tex]60\°-53\°-67\°[/tex]
In the triangle FGH
Find the measure of angle G
[tex]m<F+m<G+m<H=180\°[/tex]
substitute the values and solve for m<G
[tex]60\°+m<G+67\°=180\°[/tex]
[tex]m<G=180\°-(60\°+67\°)=53\°[/tex]
The measures of internal angles triangle FGH are [tex]60\°-53\°-67\°[/tex]
therefore
The two triangles are similar by AAA
