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)
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