Given: DE and DF are midsegments of ABC
Prove: DE = 1/2 AC
1. midsegments DE and DF: gi...
Mathematics, 20.05.2021 17:00 mutesheep
Given: DE and DF are midsegments of ABC
Prove: DE = 1/2 AC
1. midsegments DE and DF: given
2. DF ll BC and AC ll DE: Midsegments are || to the non-included side of the Δ.
3. AB is a transversal cutting DF and BC.
AB is a transversal cutting AC and DE: definition of transversal line
4. m∠FAD = m∠EDB
m∠ADF = m∠DBE: Corresponding Angles Theorem
5. AD = BD: definition of midpoint
6. DBE ≅ ADF: ASA
7. A F = 1/2 AC: definition of midpoint
8.
9. DE = 1/2 AC: Transitive Property of Equality
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