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Can someone help me with this two column proofs? -this one is confusing to me

Don’t mind the pencil X between A/E for reflexive.
Can you finish the reason/ statement proofs for me? Thank you!

Can someone help me with this two column proofs? -this one is confusing to me Don-example-1
User Lekens
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Perpendicular bisectors have a particular property: if AB is a perpendicular bisector of CD, then every point lying on AB has the same distance from C and D.

In your case, we have that every point lying on AC has the same distance from B and D.

So, in particular, we have EB=ED, because E lies on AC.

Moreover, since AC is a perpendicular bisector, it is the height of the triangle (if we choose BD as base), and it bisects BD: this means that the triangle is isosceles, so AD=AB.

This means that triangles ABE and ADE have:

  • AD=AB because ABD is isosceles
  • EB=ED because AC is the perpendicular bisector of BD
  • AE in common

So, their sides are all equal, and thus they are congruent.

User SWalters
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