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Section 5.2 Notes

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Section 5.2 Notes Properties of special segments – PowerPoint PPT presentation

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Title: Section 5.2 Notes


1
Section 5.2 Notes
  • Properties of special segments

2
5.2 Notes
  • Find AB if is a median of ?ABC.
  • In order to find AB, we must know x.

3
5.2 Notes
  • Find AB if is a median of ?ABC.
  • If is a median, then D is the midpoint
    of AC and .

4
5.2 Notes
  • If , then set the algebraic
    expressions equal to solve for x.
  • x 3 2x - 17

5
5.2 Notes
  • x 20
  • AB 13

6
5.2 Notes
  • Find BC if is an altitude of ?ABC.
  • To find BC we need to find x so that we can find
    AD and DC and add them to get BC.

7
5.2 Notes
  • Find BC if is an altitude of ?ABC.
  • If is an altitude then and
  • is a right angle.

8
5.2 Notes
  • Find BC if is an altitude of ?ABC.
  • If is a right angle then its measure
    is 90.
  • So set 4x 10 90 to solve for x.

9
5.2 Notes
  • Find BC if is an altitude of ?ABC.
  • x 20
  • 2(20) 40, 3(20) 456, 405696
  • BC 96

10
5.2 Notes
  • Find if is an angle
    bisector of ?ABC and if

11
5.2 Notes
  • Find if is an angle
    bisector of ?ABC and if
  • We need to find x in order to find

12
5.2 Notes
  • Find if is an angle
    bisector of ?ABC and if
  • If is an angle bisector of ?ABC, then

13
5.2 Notes
  • Find if is an angle
    bisector of ?ABC and if
  • If then their measures
    are equal and the sum of their measures equal the
    measure of

14
5.2 Notes
  • Find if is an angle
    bisector of ?ABC and if
  • Find x by setting x6 x6 4x 6.

15
5.2 Notes
  • Find if is an angle
    bisector of ?ABC and if
  • x 9

16
5.2 Notes
  • A centroid of a triangle is located the
    distance from the vertex of a triangle.
  • That means that it is the distance from the
    side of a triangle.
  • If you know the length of a median, divide it by
    three.
  • That number is the distance from the centroid to
    the side, and twice that number is the distance
    from the centroid to the vertex.

17
5.2 Notes
  • If you know the distance from the centroid to the
    side, _______ to find the length of the median.
  • and ________ to find the distance from the
    centroid to the vertex.
  • If you know the distance from the centroid to the
    vertex, _______ to the get the distance from the
    centroid to the side.
  • and ________ that number to find the length of
    the median.

18
5.2 Notes
  • G is the centroid of ? ABC.

19
5.2 Notes
  • G is the centroid of ? ABC.
  • If BD 9 , then BG _____.

20
5.2 Notes
  • G is the centroid of ? ABC.
  • If AG 10 , then AF _____.

21
5.2 Notes
  • G is the centroid of ? ABC.
  • If EG 4.2 , then EC _____.

22
5.2 Notes
  • G is the centroid of ? ABC.
  • If BE 6 , then EA _____.

23
5.2 Notes
  • G is the centroid of ? ABC.
  • If BC 11 , then FC _____.

24
5.2 Notes
  • G is the centroid of ? ABC.
  • If DC , then AC _____.

25
5.2 Notes
  • P is the orthocenter of ?OPQ.

26
5.2 Notes
  • P is the orthocenter of ?OPQ.

27
5.2 Notes
  • The incenter of a triangle is equidistant from
    the sides of the triangle.

28
5.2 Notes
  • N is the incenter of ?HIJ.

29
5.2 Notes
  • N is the incenter of ?HIJ.
  • KN 8, LN _____.

30
5.2 Notes
  • N is the incenter of ?HIJ.

31
5.2 Notes
  • N is the incenter of ?HIJ.
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