Do Now Lesson Presentation Exit Ticket
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1 Do Now Lesson Presentation Exit Ticket
2 Warm Up #7 1. Is DE DF? Explain. E 61 o D 58 o F Yes; m F = 61 o by Converse of the Isosceles Thrm. 2. What is the value of x? 3. Define an angle bisector in your own words. An angle bisector divides an angle into two equal parts. 4. Draw an angle bisector. x = 4
3 You hang a bulletin board over your desk using string. The bulletin board is crooked. When you straighten the bulletin board: What type of triangle does the string form with the top of the board? How do you know? Visualize the vertical line along the wall that passes through the nail. What relationships exist between this line and the top edge of the straightened bulletin board? Explain.
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5 Connect to Mathematical Ideas (1)(F) By the end of today s lesson, SWBAT Construct a perpendicular bisector and make conjectures about the geometric relationship formed by the endpoints and points on the bisector. Construct angle bisectors and make conjectures about geometric relationships formed by the bisector and sides of the angle.
6 Vocabulary equidistant locus
7 Explore:
8 Explore: Make the conjecture
9 When a point is the same distance from two or more objects, the point is said to be equidistant from the objects. Triangle congruence theorems can be used to prove theorems about equidistant points.
10 A locus is a set of points that satisfies a given condition. The perpendicular bisector of a segment can be defined as the locus of points in a plane that are equidistant from the endpoints of the segment.
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12 Example 1: Given 7) 7) CPCTC 8) 8) Definition of Congruence
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14 Example 2: Applying the Perpendicular Bisector Theorem and Its Converse BD is the perpendicular bisector of AC, so B is equidistant from A and C. Now find: AB = BC 4x = 6x 10 2x = 10 x = 5 AB = 4x Bisector Theorem. Substitute the given values. Combine liked terms Divide both sides by 2. 4 (5) = 20
15 Example 3: Applying the Perpendicular Bisector Theorem and Its Converse A park director wants to build a T-shirt stand equidistant from the Rollin s Coaster and the Spaceship Shoot. What are the possible locations of the stand? Explain. To be equidistant from the two rides, the stand should be on the perpendicular bisector of the segment connecting the rides. Find the midpoint A of RS and draw l through A perpendicular to RS. The possible locations of the stand are all the points on line l.
16 Got It? Solve With Your Partner Problem 1 Applying Perpendicular Bisector A park director wants to build a T-shirt stand equidistant from the Paddle boats and the Spaceship Shoot. What are the possible locations? Explain. Any locus point on the perpendicular bisector of PS.
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19 Example 4: Applying the Angle Bisector Theorem and Its Converse RM = RP 7x = 2x x = 25 x = 5 Bisector Theorem. Substitute the given values. Combine liked terms Divide both sides by 5. Now find: RP = 7x 7 (5) = 35
20 Got It? Solve With Your Partner Problem 2 Applying Angle Bisectors What is the length of FB? FB= FD 6x + 3 = 4x + 9 2x = 6 Bisector Theorem. Substitute the given values. Combine liked terms Now find: x = 3 FB = 6x + 3 Divide both sides by 3. 6(3) + 3 = 21
21 Closure: Communicate Mathematical Ideas (1)(G) What statement describes the points on the perpendicular bisector of a segment? They are equidistant from the endpoints of the segment. What statement can be made about a point on the bisector of an angle? It is equidistant from the sides of the angle. What are the similarities and differences between an angle bisector and a perpendicular bisector?
22 Exit Ticket: Apply Mathematics (1)(A) Use the diagram for Items Given that m ABD = 16, find m ABC. 2. Given that m ABD = (2x + 12) and m CBD =(6x 18), find m ABC. 3. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints X(7, 9) and Y( 3, 5).
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