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Bell Ringer

Bell Ringer. Write a 2 column proof Given: Segment BD is the perpendicular bisector of segment AC Prove:  ADB   CDB. Isosceles Triangle Theorem. If a triangle is isosceles, then the base angles are congruent.

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Bell Ringer

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

  2. Isosceles Triangle Theorem • 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 Step 1: write the statement in conditional form Step 2: Identify the “given” and “prove” The base angles of an isosceles triangle are congruent.

  3. Step 3: Draw and label a picture Given: Segment AM is a median Prove: <C is congruent to <T Step 4: If necessary, draw in additional parts to assist with the proof

  4. Step 5: Plan the proof

  5. Step 6: Write the Proof

  6. 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 Any point on the perpendicular bisector of a line segment is equidistant from the endpoints of a segment.

  7. Step 3: Draw and label a picture 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

  8. Step 5: Plan the proof

  9. Step 6: Write the Proof

  10. 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!)

  11. Homework • 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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