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Bell Ringer

Bell Ringer. Angle Bisector and Perpendicular Bisector. Distance From A Point to A Line . The distance from a point to a line is measured by the length of the perpendicular segment from a point to the line. :. Equidistant.

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Bell Ringer

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  1. Bell Ringer

  2. Angle Bisector and Perpendicular Bisector

  3. Distance From A Point to A Line • The distance from a point to a line is measured by the length of the perpendicular segment from a point to the line. :

  4. Equidistant • Equidistant is when a point is the same distance from one line as it is from another line, the point is equidistant from the two lines. :

  5. WU  WU Angle Bisector Theorem 4. WV  WT Example 1 Use the Angle Bisector Theorem Prove that∆TWU  ∆VWU. UW bisectsTUV.∆UTW and∆UVW are right triangles. ∆TWU  ∆VWU. SOLUTION Statements Reasons 1. Given 1. UWbisectsTUV. 2. ∆UTWand∆UVW are right triangles. 2. Given 3. Reflexive Prop. of Congruence 3. 4. HL Congruence Theorem 5. ∆TWU ∆VWU 5.

  6. Perpendicular Bisector • PerpendicularA segment, ray, or line that is perpendicular to a segment at its midpoint. :

  7. Example 2 Use Perpendicular Bisectors Use the diagram to find AB. SOLUTION In the diagram, AC is the perpendicularbisector of DB. AB = 8x = 8 · 4 = 32 ANSWER By the Perpendicular Bisector Theorem, AB = AD. 8x = 5x +12 3x = 12 Subtract 5x from each side. Divide each side by 3. = x = 4 3x Simplify. 12 3 2 You are asked to find AB, not just the value of x.

  8. Use Angle Bisectors and Perpendicular Bisectors Now You Try  Find FH. 1. 5 ANSWER Find MK. 2. 20 ANSWER 3. Find EF. 15 ANSWER

  9. Example 3 Use the Perpendicular Bisector Theorem In the diagram,MNis the perpendicular bisector of ST.Prove that ∆MSTis isosceles. SOLUTION To prove that∆MST is isosceles, show that MS = MT. Statements Reasons MN is the bisector of ST.  1. 1. Given Perpendicular Bisector Theorem 2. 2. MS =MT ∆MST is isosceles. Def. of isosceles triangle 3. 3.

  10. Now You Try 

  11. Now You Try 

  12. Page 276

  13. Complete Page 277-278 #s 10-24 & 32 even Only

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