Another Check & Possbile Site?

Question

First of all, i'd like to ask if you can refer to any sites with geometric proof problems and solutions so that i can practice.

second am i correct?:
Given: line CP is perpendicular bisector of segment AB
Prove: CA = CB

..................C
................/..|..&#92;
............../....|....&#92;
............/......|......&#92;
........A/____.|.____&#92;B
...................P

Note: it should show that there's a right angle at CPB and that AP = PB 

Now my proof:
1) given: line CP is perpendicular bisector of segment AB
2) def of Perpendicular bisector:  <APC = <CPB
3) reflexive Prop: segment PC = Segment PC
4) SAS prostulate: Triange ACP is congruent to triange CPB
5) corresponding parts of triangle:  CA = CB

Mewtwo · Accepted Answer

Your proof is NOT correct. Before listing any sites, let's give a correct proof first.

(1) line CP is perpendicular bisector of segment AB (Given)
(2) AP = BP and angle CPA and angle CPB are right angles (Def. of Perpendicular Bisector)
(3) angle CPA and angle CPB are congruent (All right angles are congruent.)
(4) CP = CP (Reflexivity)
(5) triangle CPA is congruent to triangle CPB (SAS Postulate)
(6) CA = CB (Corresponding parts of congruent triangles are congruent.)

This completes the proof. It looks like you may benefit from a little extra practice, but websites are not enough. You will need someone who can help you to check your logic. Proof writing is something that is not easy to learn; but with someone else checking you, it becomes much easier. Some websites that you may check out are:

(A) http://www.wyzant.com/Help/Math/Geometry/Introduction/Two_Column_Proofs.aspx
(B) http://www.wikihow.com/Write-a-Congruent-Triangles-Geometry-Proof
(C) http://www.funtrivia.com/trivia-quiz/SciTech/Writing-a-Two-Column-Proof-207695.html

Shannon · Answer

You are wrong in your proof.
When you use SAS, SSA, etc. you MUST have the three components in your proof before the postulate. Also, your definition of perpendicular bisector is flawed.

A perpendicular bisector bisects a line at a right angle. Therefore, AP and PB are congruent. Put that in your proof.
Also, in 2), you incorrectly jump to the conclusion that <APC = <CPB. You must first say that because it is a P.B., angles APC and CPB are both right angles. Then, because all right angles are congruent, APC and CPB are congruent.
After that, you may put in the SAS postulate.

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Another Check & Possbile Site?

2 Answers