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 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. :

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

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

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

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

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

Now You Try 

Now You Try 

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