Section 14.4: Perpendicular Lines

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Presentation transcript:

Section 14.4: Perpendicular Lines

Objective: By following instructions, students will be able to: Learn the key ideas about perpendicular bisectors of a segment.

Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

explain 1 Given: P is on the perpendicular bisector m of 𝐴𝐵 . Prove the Perpendicular Bisector Theorem Given: P is on the perpendicular bisector m of 𝐴𝐵 . Prove: PA = PB

Your-Turn #1 What conclusion can you make about △KLJ in the diagram using the Perpendicular Bisector Theorem?

Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.

explain 2 Proving the Converse of the Perpendicular Bisector Theorem Given: PA = PB Prove: P is on the perpendicular bisector m of 𝐴𝐵 .

Your-Turn #2

explain 3A Prove the theorem below about right angles. If two lines intersect to form one right angle, then they are perpendicular and they intersect to form four right angles.

explain 3B Prove the theorem below about right angles. If two intersecting lines form a linear pair of angles with equal measures, then the lines are perpendicular.

Your-Turn #3

Revisit Objective: Did we… Learn the key ideas about perpendicular bisectors of a segment?

HW: Sec 14.4 pg 532 #s 5-14