DO NOW Take out a protractor Take out your compass Put your 2.6 Worksheet on your desk ready to be stamped. In the picture to the left, solve for x. Then find the angle measures. Announcements Test next Wednesday over angle relationships and constructions. Vocab and review (on website) are due Wednesday. Tutoring Tuesdays/Thursdays Test corrections from Unit 1 are due next Friday. Duplicating Segments and Angles, Constructing Perpendicular Bisectors 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 Creating Geometric Figures Sketch—Freehand, “looks like,” not accurate Draw—Carefully use a straightedge and use measurements from protractor, fairly accurate. Construct—Don’t rely on protractor measurements. Use compass and straightedge. Guaranteed to be accurate. Duplicating a Segment Step 1: Draw segment AB. Step 2: Draw a ray starting at C. Step 3: Open your compass to match the length of AB. Step 4: Put the point of your compass on point C and drag the pencil to make an arc that intersects the ray. Step 5: Mark the intersection D. AB ≅ CD Duplicating an Angle Step 1: Draw ∠DEF. Step 2: Draw a ray from point G. Step 3: With your compass, put an arc around E that intersects the rays ED and EF. Step 4: Without changing the width of your compass, put a matching arc around G. Step 5: Open your compass to measure the distance between intersection points in ∠DEF. Step 6: Mark the same distance from the intersection point in G through the arc. Step 7: Draw a ray from G to the new intersection point. ∠E ≅ ∠G Practice Draw a segment that is 5cm (with ruler measurements). Construct a duplicate segment (without ruler measurements, only using a compass and straightedge). Practice Draw an angle that is 70o (using a protractor) Construct a duplicate angle (not using a protractor). 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. Stations! Direct: Practice Constructions Collaborative: Without writing on the worksheets, complete 3.1 and 3.2 worksheets on a separate sheet of paper as a group. (Each person turn in your own paper.) 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. 1. Draw an obtuse angle. Label it ∠LGE, then duplicate it. 2. Draw a line segment. Label it RS, then duplicate it. 3. Draw a line segment. Label it PQ, then construct its perpendicular bisector. 4. Draw two acute angles. Construct a third angle with measure equal to the sum of the measures of the first two angles. You may not use a protractor. Exit Slip Honors For all exercises, do not erase your construction marks. 1. Draw an obtuse angle. Label it ∠LGE, then duplicate it. 2. Draw a line segment. Label it PQ, then construct its perpendicular bisector. 3. Draw two acute angles. Construct a third angle with measure equal to the sum of the measures of the first two angles. You may not use a protractor. 4. Draw a quadrilateral QUAD. Duplicate it, matching all the angles AND segments. Label the construction COPY so that QUAD ≅ COPY.