Write a 2 column proof Given: Segment BD is the perpendicular bisector of segment AC Prove:  ADB   CDB.

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Presentation transcript:

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)