Given that B is the midpoint of AC, and E is the midpoint of AD, prove △ABE and △ACD are similar. The figure shows triangle A C D. Point B lies on side A C. Point E lies on side A D.

1.B is the midpoint of AC⎯⎯⎯⎯⎯ and E is themidpoint of AD⎯⎯⎯⎯⎯. (Given)2.AB⎯⎯⎯⎯⎯≅BC⎯⎯⎯⎯⎯,AE⎯⎯⎯⎯⎯≅ED ⎯⎯⎯⎯⎯(Def. of mdpt.)3. ACAB=ADAE(Trans. Prop. of =)4.∠A≅∠A(Reflex. Prop. of ≅)5.ΔABE∼ΔACD(SAS∼)

1.B is the midpoint of AC⎯⎯⎯⎯⎯ and E is themidpoint of AD⎯⎯⎯⎯⎯. (Given)2.AB⎯⎯⎯⎯⎯≅ED⎯⎯⎯⎯⎯,AE⎯⎯⎯⎯⎯≅BC ⎯⎯⎯⎯⎯(Def. of mdpt.)3. ACAB=ADAE(Trans. Prop. of =)4.∠A≅∠A(Trans. Prop. of =)5.ΔABE∼ΔACD(AA∼)

1.B is the midpoint of AC⎯⎯⎯⎯⎯ and E is themidpoint of AD⎯⎯⎯⎯⎯. (Given)2.AB⎯⎯⎯⎯⎯≅ED⎯⎯⎯⎯⎯,AE⎯⎯⎯⎯⎯≅BC ⎯⎯⎯⎯⎯(Def. of mdpt.)3. ACAB=AEAD(Reflex. Prop. of ≅)4.∠A≅∠A(Trans. Prop. of =)5.ΔABE∼ΔACD(SAS∼)

1.B is the midpoint of AC⎯⎯⎯⎯⎯ and E is themidpoint of AD⎯⎯⎯⎯⎯. (Given)2.AB⎯⎯⎯⎯⎯≅BC⎯⎯⎯⎯⎯,AE⎯⎯⎯⎯⎯≅ED ⎯⎯⎯⎯⎯(Def. of mdpt.)3. ACAB=ADAE(Trans. Prop. of =)4.∠A≅∠A(Reflex. Prop. of ≅)5.ΔABE∼ΔACD(AA∼)