Question 762102: I need help with a geometry proof please!
Given: Angle BAC is a right angle; Angle DEC is a right angle; Line BD bisects Line AE.
Prove C is the midpoint
Here's what I have so far:
Angle BAC is a right angel, angle DEC is a right angle--Given
Angle BAC=Angle DEC: Right angles are congruent
Segment BD bisects Segment AE: Given
Since Segment BD bisects Segment AE, AC=CE: Line Bisector
Triangle BAC=Triangle DEC: ASA
BC=CD: CPCTC
BC=CD: C is the midpoint of BD
I must prove another angle to use ASA or change my proof.
I've had help to get this far since I have never been good at doing proofs!
Thank you for your help!
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website! You're almost there :)
Yes, you need to prove that BAC and DEC are congruent using ASA.
You already showed that AC = CE and Angle BAC = angle DEC.
Now, angle DCE is also equal to angle BCA because they are *vertical angles* formed by the intersection of lines AE and BD. (When two lines intersect, the vertical angles formed are congruent, and the adjacent angles add up to 180)
Now we can apply ASA theorem since we have 2 angles and the included side as equal.
BAC and DEC are congruent triangles. So, BC = CD (corresponding sides), and hence C is the midpoint.
:)
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