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DB is perpendicular to AE at C, AB is congruent to DE, and C is the midpoint of AE. Prove DE is parallel to AB

DB is perpendicular to AE at C AB is congruent to DE and C is the midpoint of AE Prove DE is parallel to AB class=


Answer :

Medunno13

1. [tex]\overline{DB}[/tex] is perpendicular to [tex]\overline{AE}[/tex] at [tex]C[/tex] (given)

2. [tex]\angle ACB[/tex] and [tex]\angle DCB[/tex] are right angles (perpendicular lines form right angles)

3. [tex]\triangle ACB[/tex] and [tex]\triangle DCE[/tex] are right triangles (a triangle with a right angle is a right triangle)

4. [tex]C[/tex] is the midpoint of [tex]\overline{AE}[/tex] (given)

5. [tex]\overline{AC} \cong \overline{CE}[/tex] (definition of midpoint)

6. [tex]\overline{AB} \cong \overline{DE}[/tex] (given)

7. [tex]\triangle ACB \cong \triangle ECB[/tex] (HL)

8. [tex]\angle BAC \cong \angle DEC[/tex] (CPCTC)

9. [tex]\overline{DE} \parallel \overline{AB}[/tex] (converse of alternate interior angles theorem)

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