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Mastering 2 Column Proofs: Isosceles Triangle Theorems & Perpendicular Bisector Theorems

Enhance proof-solving skills with detailed steps, examples, and practice problems on isosceles triangles and perpendicular bisectors. Learn to identify given statements and proofs, draw diagrams, and construct convincing mathematical arguments entirely in 2-column format.

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Mastering 2 Column Proofs: Isosceles Triangle Theorems & Perpendicular Bisector Theorems

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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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