Unit 1 All About Angles and Constructions (not necessarily in that order) Ms. Houghton Geometry Honors Fall 2014.

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Presentation transcript:

Unit 1 All About Angles and Constructions (not necessarily in that order) Ms. Houghton Geometry Honors Fall 2014

Draw a line m such that it is a longer Than line segment AB and mark a Point C on line m Take your compass and put the tip on A, and the pencil on point B. Keeping your compass the same, put the point on point C, and create an arc that crosses through line m Call it point D mm m

Duplicate a line segment AB and construct a line segment that is twice the length of line segment AB

Construction of a Segment Bisector To construct a line segment bisector: 1.Put the tip of your compass on point A, and the pencil between the midpoint and point B and draw the arc.

2. Keep the compass the same, and repeat with the tip on point B. Construction of a Segment Bisector (continued)

3) Draw a line through the intersection of the two arcs Construction of a Segment Bisector (continued)

Objectives Name Angles Classify angles Duplicate an angle using a compass and a straightedge Construct angle bisector

Vocabulary Angle Sides of an angle Vertex of an angle Protractor Degrees Acute Angle Right Angle Obtuse Angle Straight Angle Congruent Angle Duplicate an Angle Bisect Angle Bisector

How do we name angles?

Classifying Angles

Angle Pairs Complimentary Angles – 2 angles whose sum is 90° Supplementary Angles – 2 angles whose sum is 180° Linear Pair– 2 angles whose sides form a straight line and share a vertex Vertical Angles – 2 angles who share a vertex and whose sides create 2 sets of straight lines. Adjacent Angles – 2 angles who share a side and the vertex

Angle Addition Postulate

Step 1: Draw a ray with endpoint C. Step 2: Placing the point of your compass on point A, draw an arc of any size that intersects both sides of the angle..

Step 4: Using your compass, measure the distance between the intersections on angle A. E

Step 5: Keeping that distance, drawn an arc from point E, that will interest your previous arc. Step 6: Draw a line from point C to the intersection of the two arcs, point F.

Constructing an Angle Bisector An angle bisector is a line or ray that divides an angle into two congruent angles (angles of equal measure Step 1 Draw an angle Step 2: Place the compass at point C. Draw an arc that intersects both sides of the angle,. Labe the intersections point A and point B

Step 4: Place the compass at point A, and draw an arc in the interior of the angle. Repeat with the compass at point B using the same measurement of the compass. Step 5: Label the intersection of the two arcs, point D, and use a straightedge to draw a ray through points C and D.