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.