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Comments on your proof:
Two column proof.
Given: CD is an altitude of ABC, D is the midpoint of BA,
Prove: Triangle CDA = Triangle CDB
What i think is
1. CD is an altitude of ABC - Given
2. D is the midpoint of BA. - Given
3. Angle ACD = Angle BCD - def of bisected angle <----- The condition says nothing about bisection angle. It is not given
4. Angle CD = Angle CD - reflexive property <----- What angle? Three symbols are used to call for an angle.
5. Triangle CDA = Triangle CDB - AAS. <----- I'd consider this proof as false.
Am i missing something?
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Now consider this proof:
Triangles CDA and CDB have the common side CD.
They have congruent sides DB and DC (since D is midpoint of BA).
The angles CDA and CDB are congruent, since they both are direct angles.
Hence, the triangles CDA and CDB are congruent, in accordance with the SAS test for triangles.
Yes, it is written not in two column form - sorry.