Question

△efg and △hij are shown below.which statement is true?△efg is similar to △hij.

Explanation:

Step1: Calculate the third angle of \(\triangle EFG\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle EFG\), if \(\angle E = 78^{\circ}\) and \(\angle G=47^{\circ}\), then \(\angle F=180^{\circ}-(78^{\circ} + 47^{\circ})=180^{\circ}-125^{\circ} = 55^{\circ}\)

Step2: Calculate the third angle of \(\triangle HIJ\)

For \(\triangle HIJ\), if \(\angle H = 78^{\circ}\) and \(\angle I = 57^{\circ}\), then \(\angle J=180^{\circ}-(78^{\circ}+57^{\circ})=180^{\circ}-135^{\circ}=45^{\circ}\)

Step3: Check the similarity condition

Since the angles of \(\triangle EFG\) (\(78^{\circ},47^{\circ},55^{\circ}\)) and \(\triangle HIJ\) (\(78^{\circ},57^{\circ},45^{\circ}\)) are not equal in proportion (i.e., \(\angle E=\angle H = 78^{\circ}\), but \(\angle G
eq\angle I\) and \(\angle F
eq\angle J\)), \(\triangle EFG\) is not similar to \(\triangle HIJ\)

Answer:

The statement “\(\triangle EFG\) is similar to \(\triangle HIJ\)” is False.