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 In Chapter 1, you learned the definition of a midpoint of a segment. What do you think a midsegment of a triangle is?  Find the midpoint of AB: o A(-2,

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Presentation on theme: " In Chapter 1, you learned the definition of a midpoint of a segment. What do you think a midsegment of a triangle is?  Find the midpoint of AB: o A(-2,"— Presentation transcript:

1  In Chapter 1, you learned the definition of a midpoint of a segment. What do you think a midsegment of a triangle is?  Find the midpoint of AB: o A(-2, 3), B(4, 1) o A(0, 5), B(3, 6)

2  I can use properties of midsegments to solve problems. I can use properties of perpendicular bisectors and angle bisectors.

3  There are two special relationships between a midsegment of a triangle and the third side of the triangle. Triangle Midsegments Theorem TheoremIf…Then… If a ________________ ________________ of two sides of a triangle, then the segment is ________________ ________________ ________________. D is the midpoint of CA and E is the midpoint of CB

4  What are the three pairs of parallel segments in triangle DEF?

5  In triangle XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of ZX. What are the three pairs of parallel segments?

6  What are the three pairs of parallel segments in triangle DEF?

7  In triangle QRS, T, U, and B are midpoints. What are the lengths of TU, UB, and QR?

8  In the figure, AD = 6 and DE = 7.5. What are the lengths of DC, AC, EF, and AB?

9  In triangle RST, G, H, and K are midpoints. If RS = 28, GH = 20, and RH = 22, what is the length of KH, ST, and GK?

10  Complete the three application problems. 1.. 2.. 3.

11  In the diagram below on the left, CD is the perpendicular bisector of AB. CD is perpendicular to AB at its midpoint. In the diagram below on the right, CA and CB are drawn to complete triangle CAD and triangle CBD.

12  A point is _______________from two objects if it is the same distance from the objects. So point C is _____________ from points A and B.

13  There is a special relationship between the points on the perpendicular bisector of a segment and the endpoints of the segment. Perpendicular Bisector Theorem TheoremIf…Then… If a point is on the perpendicular bisector of a segment, then it is equidistance from the endpoints of the segment. Converse of the Perpendicular Bisector Theorem TheoremIf…Then… If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

14  BD is the perpendicular bisector of AC, so B is equidistant from A and C.

15  What is the length of QR?

16  What is MN?

17 Angle Bisector Theorem TheoremIf…Then… If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. Converse of Angle Bisector Theorem TheoremIf…Then… If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

18  What is the length of RM?

19  What is the length of FB?

20  What is the length of OP?

21 1. Which segment is parallel to JK? 2. If LK = 46, what is NM? 3. If JK = 5x + 20 and NO = 20, what is the value of x? 4. What is the relationship between AC and BD? 5. What is the length of AB? 6. What is the length of DC?

22  Page 288, #8-26, 32, 34 and Page 296, #6-9 all, 12-22 all

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