Chapter 1: Tools of Geometry

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Presentation transcript:

Chapter 1: Tools of Geometry 1-7 Basic Constructions

Constructions uses a straightedge and a compass to draw a geometric figure what career would this be useful?? straightedge: ruler with no markings on it compass: geometric tool used to draw circles and arcs

Construction #1: congruent segments you will be given a segment to “copy” steps: draw a ray (with an endpoint) measure the original segment with the compass leave the compass open and draw an arc on your ray label the point where the ray and arc intersect

Try it!! On your notes, there is a segment to copy Work through the steps with me

Construction #2: congruent angles you will be given an angle to copy steps: draw a ray like before on the original angle open your compass and draw an arc that intercepts both sides of the angle leave your compass open the same length and draw that arc on the ray measure on the original angle the distance between the intersections mark this length on the ray (I will show you) connect the arc intersection with the endpoint of the ray

Try it!! On your notes, there is an angle to copy Work through the steps with me

Bisectors perpendicular lines: bisector: cuts something in half perpendicular bisector: a line/segment/ray that is perpendicular to the segment at its midpoint

Construction #3: perpendicular bisector you will be given a segment steps: put the end of the compass on one end of the segment open the compass to more than half of the segment and make an arc keep that length and move your compass to the other endpoint and make another arc draw a line between the intersections of the arc

Try it!! On your notes, there is a segment to bisect Work through the steps with me

Construction #4: angle bisector you will be given an angle steps: open your compass and draw an arc through both sides of the angle measure the distance between intersections, and then open the compass a little larger make an arc at that length in the middle of the angle from both intersections draw a line from the vertex of the angle to the small arc intersection

Try it!! On your notes, there is an angle to bisect Work through the steps with me

Example 4 KN bisects angle JKL. Solve for x and find the measure of angle JKN.

Homework!! p. 47-49 1-8, 10-17, 22-24