1. Chapter 5: Properties of Triangles Section 5.1: Perpendiculars and Bisectors

2. perpendicular bisector – a segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

3. equidistant from two points – a point is equidistant from two points if its distance from each point is the same.

4. Theorem 5.1: Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. C A P B If CP is the perpendicular bisector of AB, then CA = CB.

5. Theorem 5.2: Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. C P A B D If DA = DB, then D lies on the ┴ bisector of AB.

6. distance from a point to a line – is defined as the length of the perpendicular segment from the point to the line. Q P m equidistant from the two lines - when a point is the same distance from one line as it is from another line.

7. Theorem 5.3: Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. If m BAD = m CAD, then DB = DC.

8. Theorem 5.4: Converse to the Angle Bisector Theorem If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle. If DB = DC, then m BAD = m CAD.

9. Example 1: In the diagram shown, PQ is the perpendicular bisector to CD. T 7 7 C Q D P a.What segment lengths in the diagram are equal? QC = QD; PC = PD; TC = TD b.Explain why T in on PQ. CT = DT, so T is equidistant from C and D. By Theorem 5.2, T is on the ┴ bisector of the segment.

10. Example 2: In the diagram, CD is the perpendicular bisector of AB. C A D B a.What is the relationship between AD and BD? AD is congruent to BD b.What is the relationship between angles ADC and BDC? They are congruent and they both equal 90°.

11. HOMEWORK pg. 268 – 269; 8 – 13, 16 – 17, 19, 21 – 26