agenda 1) bell work 2) outcomes 3) finish 8.4 and 8.5 notes 4) 8.6 -triangle proportionality...
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Agenda• 1) Bell Work• 2) Outcomes• 3) Finish 8.4 and 8.5 Notes• 4) 8.6 -Triangle proportionality theorems• 5) Exit Quiz• 6) Start IP
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Bell Work• 1) Are the triangles similar? If so, explain
why.
• 2) Solve for the missing variable• a) b)
• 3) Write a statement of proportionality for the similar figures below:
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Outcomes• I will be able to:
• 1) Use ratios and proportions to find missing side lengths of similar figures
• 2) Understand intersections of parallel lines and triangles
• 3) Use proportionality theorems to find missing lengths
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Socrative Student Review• 1) Are the following triangles similar? • A) Yes, by AA• B) Yes, by SAS• C) Yes, by SSS• D) not similar
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Socrative Student Review
• 2) Solve for the missing variable if the figures are similar.
• A) 10• B) 12
C) 14• D) 20
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Socrative Student Review
• 3) Are the following triangles similar?• A) Yes, by AA• B) Yes, by SAS• C) Yes, by SSS• D) not similar
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Socrative Student Review
• 4) Solve for the missing variable if the figures are similar.
• A) 15• B) 30 • C) 36• D) 40
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Socrative Student Questions
• 5) Write a statement of proportionality if the figures are similar.
• A)• B)ABCD ~ MNOP• C)• D)
PO
AB
CB
ON
MN
DC
MP
AD
MP
AD
OP
DC
NO
CB
MN
AB
PDOC
NBMA
;
;;
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Proportions and Similar Triangles (8.6)
• Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
• Meaning:
TR
QT
UR
SU
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Proportions and Similar Triangles
• Converse of the Triangle Proportionality Theorem: If a line divides two sides of a triangle proportionally, then the line is parallel.
• Meaning:
• So, QS is parallel to TUTR
QT
UR
SU
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Example
4
2
2.5
x
x
4
2
5.2 X = 3.2
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On Your OWN
20
8
25
10
Cross multiply: 200 = 200
So, yes, EB is parallel to DC
20 8
25
10
Use the converse of thetriangle proportionalitytheorem.
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Theorem 8.6• Theorem 8.6: If three parallel lines intersect
two transversals, then they divide the transversals proportionally.
• Meaning:XZ
VX
WY
UW
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Theorem 8.7• Theorem 8.7: If a ray bisects an angle of a
triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other to sides
• Meaning:
BC
AC
DB
AD
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Examples
2.4 1.42.2
2.2x
y
z
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On Your OWN
• Find the value of x
9
102
6
4 x
36 = 12x – 60X = 8
How do we set this up?
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Example
x
14 - x
9
15
14
xx
How do we set this up?
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On Your OWN
• Solve for p
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Exit Quiz• 1) Solve for the variable
• 2) Solve for the variable
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IP
• Worksheet over triangle proportionality• Due Friday• Also, Friday, we will go over the quizzes
from last week
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Chapter 8 Review (Ratios)• ***Remember, in order to have a ratio, we
must make sure that each part of the ratio is in the same units
• Example:
• Remember to always move to the smallest unit
5
6
in
ft
5 5
6 12 72
in in
ft in in
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Chapter 8 Review (proportions)
• Remember, proportion rules• If then…
• 1) Reciprocal property
• 2)
• 3)
a c
b d
b d
a c
a b c d
b d
a b
c d
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Chapter 8 Review (geometric mean)
• Geometric mean:
• x =
• Example: Find the geometric mean of 6 and 8
• x = = ***Remember to reduce (see board)
a x
x b
a b
6 8 48
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Chapter 8 Review (Similar Figures)• Similar Figures must have congruent
angles and side ratios that are proportional
• Similarity Statement:
• Statement of Proportionality
AB BC CD AD
EF FG GH EH
EFGHABCD ~
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Chapter 8 Review (Similar Figures)
• Scale Factor: The ratio of corresponding sides in similar figures
• ***Used to find all the missing pieces in similar figures
• ***May be used to find the perimeter of similar figures
• See examples throughout notes
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Chapter 8 Review (Similar Triangles)• There are three ways to prove triangles
are similar:• AA – When you know two angles from the
two triangles are congruent to each other
• Example:• Each triangle has
a right angle• And vertical angles
are congruent Triangles similar by AA
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Chapter 8 Review (Similar Triangles)• SSS – When all three side ratios are equal
to each other
• Do these ratios equal each other?• Yes, similar by SSS
6 7 8
12 14 16
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Chapter 8 Review (Similar Triangles)• SAS – When one angle is congruent and
the side ratios of that included angle are equal to each other
• We know one angle is congruent.
• Check side lengths:
• Yes, similar by SAS7 8
14 16