Understanding Segment and Angle Bisectors: Midpoints and Geometry Concepts
This learning module focuses on the concepts of segment and angle bisectors, guiding students to effectively utilize the midpoint formula. Students will learn to find midpoints between two endpoints, determine an endpoint when given the midpoint, and understand the difference between intersecting and bisecting. The module includes discussion prompts, practical examples, and exercises that reinforce these concepts. By the end, learners will have a comprehensive understanding of how to find and work with midpoints in geometry.
Understanding Segment and Angle Bisectors: Midpoints and Geometry Concepts
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Presentation Transcript
Geometry SEGMENT AND ANGLE BISECTORS
Learning Outcomes • I will be able to use the midpoint formula to find the midpoint between two given endpoints • I will be able to find one endpoint given the other endpoint and the midpoint • I will be able to tell the difference between intersect and bisect
Think-Pair-Share • Where is the middle of this segment? (1,4) (-3,-1)
Think-Pair-Share • Where is the middle of this segment? (1,4) (-3,-1)
How would you consistently find the middle of two numbers? Let’s use 10 and 20 as an example. • Find the average! • For example: • 10 + 20 = 30 • 30/ 2 = 15
Midpoint formula • Take the average of the x’s and y’s
Midpoint Formula • Where is the middle of this segment? • - (1,4) • 1 (2, 3) (- , 1 ) (-3,-1) (-3, -1)
Find the midpoint • (-2, 5) and (4, 1) • , • , • (1, 3)
Find the endpoint The midpoint of RP is M(2, 4). One endpoint is R(-1,7). How can I find the other endpoint?
midpoint • The of a segment is a point that divides, or bisects, the segment into two congruent segments. • Bisects = cut in half. When drawing a midpoint, you must have congruence marks!!!
Think-Pair-Share What can you bisect? • Segment? • Line? • Ray? • Plane? • Angle?
Segment bisector Point M is the midpoint of segment AB C A B M D Line CD is the segment bisector A segment bisector is a segment, ray, line or plane that intersects a segment at the midpoint.
Angle bisector • Ray BD bisects angle ABC D A B C
Rule 2.00: The Strike Zone • The STRIKE ZONE is that area over home plate the upper limit of which is a horizontal line at the midpoint between the top of the shoulders and the top of the uniform pants, and the lower level is a line at the hollow beneath the kneecap. The Strike Zone shall be determined from the batter's stance as the batter is prepared to swing at a pitched ball.
Hits: 2033 Homeruns: 439 Batting Avg: .328
Ichiro is also one of the best hitters Hits: 2390 Homeruns: 93 Batting Avg: .327
Height: 6’3” Weight: 230 lbs Height: 5’9” Weight: 170 lbs
61.58 in ? 40.22 in 19.11in
60.23 in ? 39.8 in 18.2 in
Solution 61.58 + 40.22 = 101.8 in 101.8/2 = 50.9 in 50.9-19.11 = 31.79 in
Solution 60.23 + 39.8 = 100.03 in 100.03/2 = 50.015 in 50.015 – 18.2 = 31.815 in
Solution • 31.79 in. for Ichiro vs. 31.815 in. for pujols
Practice Find the midpoint between the two points
practice Find ∠DEG
practice Find ∠DEF
practice Find x
practice Find ∠ABD
practice Find ∠DBC
Exit Ticket • Homework • PG. 38 17-33, 37-42, 44-49, 63-66 Find ∠DEF
