Question

proving similar triangles
what additional information is needed to prove that the
irangles are similar?
to prove △def - △jkl by sas, we would need to
show that de/jk =
to prove △def - △jkl by aa, we would need to
show that angle e ≅ or that angle f ≅

Explanation:

Step1: Recall SAS similarity criterion

For two triangles \( \triangle DEF \) and \( \triangle JKL \) to be similar by SAS (Side - Angle - Side) similarity, we need the ratio of two corresponding sides to be equal and the included angles to be congruent. We know \( \angle D\cong\angle J \). So, if \( \frac{DE}{JK}=\frac{DF}{JL} \), then \( \triangle DEF\sim\triangle JKL \) by SAS.

Step2: Recall AA similarity criterion

For two triangles \( \triangle DEF \) and \( \triangle JKL \) to be similar by AA (Angle - Angle) similarity, we need two pairs of corresponding angles to be congruent. We already know \( \angle D\cong\angle J \). If \( \angle E\cong\angle K \), then \( \triangle DEF\sim\triangle JKL \) (since the sum of angles in a triangle is \( 180^{\circ}\), the third angles will also be congruent). Also, if \( \angle F\cong\angle L \), then \( \triangle DEF\sim\triangle JKL \) by AA (because \( \angle D\cong\angle J \) and \( \angle F\cong\angle L \))

Answer:

• For SAS: \( \frac{DF}{JL} \)
• For AA: \( \angle K \), \( \angle L \)