### Lesson 6.5 ppt.

```Welcome to Geometry B!
w3 m ke i+ c unt
 This Week at a Glance
 Return Ch. 6 Quizzes
 6.5 Notes
 Assignment: 6.5 Worksheet
 Monday: 6.5 Altitudes & Angle Bisectors
 Tuesday: Ch. 6B Review
 Wednesday: Ch. 6B Test
 Friday: 7.1 Geometric Means
 Monday: 6.5 Altitudes & Angle Bisectors
 Tuesday: Ch. 6B Review
 Wednesday: Ch. 6B Test
 Friday: 7.1 Geometric Means
• I can use proportions to find
relationships using altitudes and
angle bisectors in triangles
Think about a triangle drawn on a piece of paper being placed in a
copy machine and either enlarged or reduced.
 The copy is similar to the original triangle.
Suppose you drew in special segments of a triangle, such as the
altitudes or angle bisectors on the original.
 When you enlarge or reduce that original triangle, all of
those segments are enlarged or reduced at the same rate.
Word
Definition
 A perpendicular segment from a
ALTITUDE
vertex to the line containing the
opposite side.
ANGLE
BISECTOR
 A segment whose endpoints are one
vertex of a triangle and the opposite
side.
Example
THEOREM:
 If two triangles are similar, then the
measures of the corresponding
proportional to
altitudes are _________________
the measures of the corresponding
If SH and FJ are altitudes and RST
~ EFG, then SH
RS
FJ

EF
sides.
If AD and MQ are altitudes and
AB

MQ MN
Find FG if RST ~ EFG, SH is an altitude of RST, FJ is an
altitude of EFG. ST = 6, SH = 5, and FJ = 7.
5
6
7 x
5
7
=
6
x
5x = 42
x = 8.4
ABC ~ MNP, AD and MQ are altitudes, AB = 24, AD = 14,
and MQ = 10.5. Find MN.
14
24
14
10.5
x
10.5
=
24
x
14x = 252
x = 18
ZXY ~ TRS. Find XY, XZ, and ZY.
10 XY

5
8.7
10 XZ

5
6
10 ZY

5
13
5xy = 87
5xz = 60
5xz = 130
xz = 12
zy = 26
xy = 17.4
Find ZB if STU ~ XYZ, UA is an altitude of STU, ZB is an
altitude of XYZ, UT = 8, UA = 6, and ZY = 12.
THEOREM:
 An angle bisector in a triangle
separates the opposite side into
G
segments that have the same ratio as
the other two sides.
If GC is an angle bisector, then
AG AC
AC CB
or


GB BC
AG GB
Find the value of x.
20
7
=
24
x
20x = 168
x = 8.4
Find the value of x.
x
=
x+7
11
17
17x = 11(x + 7)
17x = 11x + 77
6x = 77
x = 12.83
Find RV and VT.
14
10
=
x+2
2x + 1
RV = 3 + 2 = 5
VT = 2(3) + 1 = 7
10(2x + 1) = 14(x + 2)
20x + 10 = 14x + 28
6x + 10 = 28
6x = 18
x=3
Find the value of x.
ASSIGNMENT
6.5 Worksheet
Skip #3, 6, 9
```