Do Now Take a protractor from the front. Take out your compass.

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Presentation transcript:

Do Now Take a protractor from the front. Take out your compass. Draw an obtuse angle. Construct (using only a compass and straightedge) a duplicate angle.

Perpendicular bisectors

Perpendicular Bisectors—Terms A segment bisector—a line, ray, or segment that passes through the midpoint of a segment. Cuts the line segment in half Perpendicular lines—intersect at a right angle. Perpendicular bisector—passes through the midpoint of a segment at a right angle. Equidistant—the same distance

Constructing Perpendicular Bisectors Step 1: Draw a line segment. Set your compass to more than half the distance between the two endpoints. Step 2: Using one endpoint as center, swing an arc on both sides of the segment. Step 3: Using the same compass setting, swing an arc from the other endpoint to intersect each arc. Step 4: Mark your two intersection points and connect them.

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

Converse of Perpendicular Bisector Conjecture If a point is equidistant from the endpoints of a segment, then it is on the _______________of the segment. perpendicular bisector Also true!

Practice Draw and label AB. Construct the perpendicular bisector of AB.

Practice Draw and label QD. Construct perpendicular bisectors to divide QD into four congruent segments.

Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

Exploring Slopes Slope of Line 1? Slope of Line 2?

Slopes of Parallel Lines have equal slopes

Equations of Parallel Lines Are these lines parallel? y=3x + 8 y=3x – 4 How do you know?

Slopes of Perpendicular Lines have opposite reciprocal slopes.

Equations of Perpendicular Lines Are these lines perpendicular? y= 5x + 7 y= 5x – 2 NO! y= ½ x – 3 y= - ½ x – 9 y= ¼ x y= 4x + 7 y= -⅓x + 2 y= 3x – 4

Derive the Expression for Slopes of Perpendicular Lines 3 1/6 -8 -1/2 3/4 -t a/b m

Stations! Direct: Practice Collaborative: Without writing on the worksheets, complete 3.1 worksheet on a separate sheet of paper as a group. (Each person turn in your own paper.) DO NOT WRITE ON IT! Independent: Take your test and your notebook and begin test corrections. If you are satisfied with your test score, begin vocabulary that is due on Wednesday.

Practice

Today’s Objectives Duplicate a line segment, an angle and a polygon Construct perpendicular bisectors and midpoints Make conjectures about perpendicular bisectors Use Problem Solving skills

Exit Slip For all exercises, do not erase your construction marks. Draw an obtuse angle. Label it ∠LGE, then duplicate it. Draw a line segment. Label it RS, then duplicate it. Draw a line segment. Label it PQ, then construct its perpendicular bisector. Line segment AB starts at A (1, 2) and ends at B (4, 0). Line segment CD starts at C (.5, -2) and ends at D (4.5, 4). Determine if these lines are perpendicular bisectors. Explain your reasoning.