Segment and Angle Bisectors

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Presentation transcript:

Segment and Angle Bisectors BIG IDEA: MEASUREMENT ESSENTIAL UNDERSTANDINGS Formulas can be used to find the midpoint of any segment in the coordinate plane. To identify special angle pairs and use their relationship to find angle measures. MATHEMATICAL PRACTICE Make sense of problems and persevere in solving them

Getting Ready In a video game, two ancient structures shoot light beams toward each other to form a time portal. The portal forms exactly halfway between the two structures. Your character is on the grid shown as a blue dot. How do you direct your character to the portal? Explain how you found your answer.

Bisect or dissect Midpoint: a point that _______________ the segment into two _______________ segments. Segment bisector: a line, segment, ray or plane that _______________ a segment at its _______________ Midpoint formula:

Bisecting a Segment 1. Find the coordinates of the midpoint of a segment with the given endpoints 2.

Bisecting a Segment 3. Find the coordinates of the other endpoint of the segment with the given endpoint and midpoint

Bisect or dissect Angle Bisector: a ____________ that divides an angle into two _________________ angles. Its endpoint is at the angle ______________ 4. is an angle bisector of . Find the two angle measures not given in the diagram. a) b)

Bisecting an Angle 5. bisects . Find the value of x and the measure of the angles.

Bisecting an Angle 6. bisects . The measures of the two congruent angles are and . Solve for x and the measure of the angles.

1.5 p. 38 4 – 12 evens, 18 – 32 evens, 38 – 54 evens, 62 – 72 evens 28 questions