Write a 2 column proof

Given: Segment BD is the perpendicular bisector of segment

AC

 

Prove: ADB CDB

 

 

 

 

 

The base angles of an isosceles triangle are congruent.

Step 1: write the statement in conditional form

Step 2: Identify the “given” and “prove”

If a triangle is isosceles, then the base angles are congruent.

(In a proof, the “if” part of the statement is the given part; the “then” part is what you are trying to prove).

(For the isosceles triangle theorem, write the given and the prove statements)

Given: If a triangle is isosceles

Prove: then the base angles are congruent

Isosceles Triangle Theorem

Given: Segment AM is a median

Prove: <C is congruent to <T

Step 3: Draw and label a picture

Step 4: If necessary, draw in additional parts to assist with the proof

What do I know? Which triangles are congruent? Give reasons.

What do I need to prove? How can I prove it?

Step 5: Plan the proof

Step 6: Write the Proof

Any point on the perpendicular bisector of a line segment is

equidistant from the endpoints of a segment.

Perpendicular Bisector Theorem

Step 1: write the statement in conditional form

Step 2: Identify the “given” and “prove”

If a point is on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of a segment.

Given: If a point is on the perpendicular bisector of a line segment

Prove: it is equidistant from the endpoints of a segment

Given: Segment SE is the perpendicular bisector of PN

Prove: Segment PS is congruent to segment SN

Step 4: If necessary, draw in additional parts to assist with the proof

Step 3: Draw and label a picture

Step 5: Plan the proof

What do I know? Which triangles are congruent? Give reasons.

What do I need to prove? How can I prove it?

Step 6: Write the Proof

Practice Problem using PBT

 

Given: segment ST is the perpendicular bisector of segment RQ.

Prove that angle SQT is congruent to angle SRT.

(Hint: Using PBT this can be done is 6 steps!)

Finish Cornell Notes (Summary) At least 3 good sentences

Study for Quiz Tomorrow (You can use your notes from 2 Column Proofs)