Mathematics, 23.02.2021 01:00 gabbymcdermid

Given that B is the midpoint of AC, and E is the midpoint of AD, prove △ABE and △ACD are similar. Options:
A. 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∼)

B. 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∼)

C. 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∼)

D. 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∼)

Given that B is the midpoint of AC, and E is the midpoint of AD, prove △ABE and △ACD are similar.

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