Geometry Unit 1: Foundations

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Presentation transcript:

Geometry Unit 1: Foundations Basic Construction

Objectives Construct copies of segments and angles. SWBAT: Construct copies of segments and angles. Construct segments, perpendicular bisectors of segments, and bisectors of angles. Apply construction to problems involving portions of segments and angles.

Rosette Challenge Using a protractor: try to recreate the image shown. A. What instructions can you give to another student so they can make a copy of your design? B. Use the tool to draw straight line segments to connect points where the circles intersect. Are any of the segments that you drew the same length? If so, why do you think they are?

Review of Congruency

Remember, with constructions, only use a ruler as a straightedge, not as a measuring tool. Copying a segment How can you copy a segment using only a straightedge and compass? Step 1: Use the straightedge to draw a line with one point Step 2: Open your compass to the width of the second point. Step 3: Draw an arc on the new line. This is your second point.

Copying an angle Step 1: Draw a ray with endpoint X Step 2: Place the compass on point A and draw an arc that intersects both rays of <A. Label the points of intersection B and C. Step 3: Without changing the setting, place the compass point at X and draw an arc intersecting the ray. Mark the point Y at the intersection. Step 4: Place the compass at point C and open it to the distance between B and C. Step 5: Without changing the setting, place the compass point at Y and draw an arc. Label the intersection point Z and use a straightedge to draw a ray from point X.

Constructing a perpendicular bisector How can you construct the perpendicular bisector of 𝘼𝘽? A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment and divides the segment into two congruent segments. You can use a straightedge and compass to construct the perpendicular bisector of a segment.

Constructing a Perpendicular Bisector Step 1: With a setting greater than 1/2AB, place the compass at point A. Draw arcs above and below segment AB. Step 2: Using the same setting, place the compass at point B. Again, draw arcs above and below AB. Step 3: Label the points of intersection and use a straightedge to connect them.

Constructing an angle bisector Step 1: Place the compass a point A and draw an arc intersecting both rays of <A. Label the points of intersection B and C. Step 2: Place the compass at Point B and draw an arc in the interior of the angle. With the same setting, place the compass at point C and draw an intersecting arc. Step 3: Label the intersections of the two arcs D and use a straightedge to draw a ray from A to D.

Essential Understanding A construction is a geometric figure produced using only a straightedge and a compass. Constructions are useful tools in geometry.