Bisecting Segments and Angles

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Presentation transcript:

Bisecting Segments and Angles Adapted from Walch Education

Bisecting a Segment A segment bisector cuts a segment in half. Each half of the segment measures exactly the same length. A point, line, ray, or segment can bisect a segment. A point on the bisector is equidistant, or is the same distance, from either endpoint of the segment. The point where the segment is bisected is called the midpoint of the segment. 1.2.2: Bisecting Segments and Angles

Bisecting a Segment Using a Compass To bisect , put the sharp point of your compass on endpoint A. Open the compass wider than half the distance of . Make a large arc intersecting . Without changing your compass setting, put the sharp point of the compass on endpoint B. Make a second large arc. It is important that the arcs intersect each other in two places. Use your straightedge to connect the points of intersection of the arcs. Label the midpoint of the segment C. Do not erase any of your markings. is congruent to . 1.2.2: Bisecting Segments and Angles

Bisecting a Segment Using Patty Paper Use a straightedge to construct on patty paper. Fold the patty paper so point A meets point B. Be sure to crease the paper. Unfold the patty paper. Use your straightedge to mark the midpoint of . Label the midpoint of the segment C. is congruent to . 1.2.2: Bisecting Segments and Angles

Bisecting an Angle An angle bisector cuts an angle in half. Each half of the angle has exactly the same measure. A line or ray can bisect an angle. A point on the bisector is equidistant, or is the same distance, from either side of the angle. 1.2.2: Bisecting Segments and Angles

Bisecting an Angle Using a Compass To bisect ∠A, put the sharp point of the compass on the vertex of the angle. Draw a large arc that passes through each side of the angle. Label where the arc intersects the angle as points B and C. Put the sharp point of the compass on point B. Open the compass wider than half the distance from B to C. Make a large arc. Without changing the compass setting, put the sharp point of the compass on C. (continued) Make a second large arc. It is important that the arcs intersect each other in two places. Use your straightedge to create a ray connecting the points of intersection of the arcs with the vertex of the angle, A. Label a point, D, on the ray. Do not erase any of your markings. ∠CAD is congruent to ∠BAD. 1.2.2: Bisecting Segments and Angles

Bisecting an Angle Using Patty Paper Use a straightedge to construct ∠A on patty paper. Fold the patty paper so the sides of ∠A line up. Be sure to crease the paper. Unfold the patty paper. Use your straightedge to mark the crease line with a ray. Label a point, D, on the ray. ∠CAD is congruent to ∠BAD. 1.2.2: Bisecting Segments and Angles

Ms. Dambreville Thanks for Watching!