#### Lesson 6.5 ppt.

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Transcript 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
Thursday: 7.0 Radical Review
Friday: 7.1 Geometric Means
Monday: 6.5 Altitudes & Angle Bisectors
Tuesday: Ch. 6B Review
Wednesday: Ch. 6B Test
Thursday: 7.0 Radical Review
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
ACB ~ MPN, then AD
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