Triangle two column proof question

In summary, the conversation discusses proving that line BD bisects angle ABC by using the given information that line BD is the perpendicular bisector of line AC. The proof involves logical steps and reasons, including the definition of a perpendicular bisector, the congruence of line segments, and the use of congruent triangles. However, the last step and reasoning need to be revised to provide a solid conclusion. It is suggested to mention the congruence of triangles more clearly and establish it as a strong supporting reason. The final conclusion should state that line BD bisects angle ABC.
  • #1
alquix
1
0
Hello! I got a problem wrong and I'm trying to figure out what happened.

it's triangle ABC bisected by line BD
Given line BD is the perpendicular bisector of line AC, Prove line BD bisects angle ABC

I got
Step 1
Line BD is the perpendicular bisector of line AC
Reason:
Given

Step 2
Line D is the midpoint of line AC
Reason:
Definition of a perpendicular bisector

Step 3
Line segment AD and line segment CD are congruent
Reason:
Definition of midpoint

Step 4
Line BD is perpendicular to line AC
Reason:
Definition of a perpendicular bisector.

Step 5
Angle ADB and CDB are right angles
Reason:
Because they are on perpendicular lines

Step 6
Angle ADB and CDB are congruent
Reason:
Right angles are always congruent

Step 7
Line BD is congruent to itself
Reason:
Reflexive property

Step 8
Line BD bisects angle ABC
Reason:
A bisector is a line which runs through the vertex of an angle and divides the angle into two congruent angles

the feedback that I got back was "The proof is easy to follow and contains many logical steps and reasons. Revision of the last step and reasoning is needed to provide a sound logical conclusion. Congruence of triangles is mentioned but has not been clearly established."

Is anyone able to explain to me where I messed up with this? I thought I did it correctly, and I'm racking my brain here!
 
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  • #2
I would use this as Step 8:
Triangles ABD and CBD are congruent.
Reason:
The tro triangles share two congruent sides (BD and AD, BD and DC) and one congruent angle (ADB and CDB).

Step 9:
Angles ABD and CBD are congruent.
Reason:
Triangles ABD and CBD are congruent.

Step 10: you conclude.
 

FAQ: Triangle two column proof question

What is a triangle two column proof?

A triangle two column proof is a method of proving that two triangles are congruent or similar by listing the corresponding parts and using geometric theorems and postulates to show that they are equal or proportional.

How do you set up a triangle two column proof?

To set up a triangle two column proof, first draw the two triangles and label all of their corresponding parts. Then, create two columns and list the corresponding parts on each side. Finally, use geometric theorems and postulates to show that the corresponding parts are equal or proportional.

What are some common geometric theorems used in triangle two column proofs?

Some common geometric theorems used in triangle two column proofs are the Angle-Angle-Side (AAS) theorem, Side-Angle-Side (SAS) theorem, Side-Side-Side (SSS) theorem, and Hypotenuse-Leg (HL) theorem.

How do you know when two triangles are congruent or similar using a two column proof?

If the two columns in the proof show that all corresponding parts are equal or proportional, then the triangles are congruent or similar. This means that the triangles have the same shape and size, but may not be in the same position or orientation.

Can you use a triangle two column proof to prove that two triangles are not congruent or similar?

Yes, a triangle two column proof can be used to prove that two triangles are not congruent or similar. If the two columns in the proof show that at least one corresponding part is not equal or proportional, then the triangles are not congruent or similar.

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