Bell Ringer

1
Bell Ringer

• Write a 2 column proof
• Given Segment BD is the perpendicular bisector
  of segment AC
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• Prove ?ADB ? ?CDB
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Isosceles Triangle Theorem

• The base angles of an isosceles triangle are
  congruent.

• 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
3
Step 3 Draw and label a picture

• Given Segment AM is a median
• Prove ltC is congruent to ltT

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

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Step 6 Write the Proof
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• 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
7

• Given Segment SE is the perpendicular bisector
  of PN
• Prove Segment PS is congruent to segment SN

Step 3 Draw and label a picture
Step 4 If necessary, draw in additional parts to
assist with the proof
8
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?

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Step 6 Write the Proof
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• Practice Problem using PBT
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• 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)