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.

CONSTRUCTIONS

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.