Download Dilations and Similarity Shortcuts

DO NOW 12/8:
Write an equation that will
show the tree’s height (h) in
terms of the shadow (s)
Dilations and
Similarity
Shortcuts
Agenda
1.
Embedded Assessment Review
2.
Triangles Cut by Parallel Lines
3.
Dilations
4.
Similarity Shortcuts: AA
5.
Debrief
Triangles Cut by Parallel Lines
 Would
triangle SET still be similar to NEW if
we “lowered” line ST to y=6?
 How is this related to our discovery about
triangle similarity shortcuts?
Triangle Proportionality Theorem
(or Side-Splitter Theorem)
“If a line is parallel to one side
of a triangle and intersects the
other two sides of the triangle,
the line divides these two sides
proportionally.”
**MUST BE IN NOTES!**
Lesson 15: Review
Lesson 15: Exit Ticket
 When
completed, turn it in for me to
check.
 If correct, congrats! You’re ready to move
on to Lesson 16.
 If incorrect, use corrections to continue
practicing Lesson 15 with Problem Set #14 before moving on to Lesson 16.
Lesson 15: Debrief
 Will
ASA work as a similarity shortcut?
Why? What about AAS?
 Why
are only two angles (AA) sufficient
evidence to prove that two triangles are
similar?
Ratio Method and Dilations
1.
2.
3.
4.
5.
Take a ruler and a piece of graph paper.
Draw any triangle ABC (use the grid!)
Pick a point P not on your triangle, and
draw a ray through each vertex.
Pick a scale factor. Increase or
decrease lines AB, .
Is the resulting triangle similar? (You can
verify using your ruler or the coordinate
grid.)
DO NOW 12/9:
Are the two triangles similar?
If so, write the similarity statement.
Similarity and
Right Triangle
Ratios
Agenda
1. Ratio Method
2. Similarity Shortcuts (AA,
ASA?, SSS, ASA?, SAS)
3. Right Triangle Ratios
4. Debrief
8
AA Similarity (Angle-Angle)
If 2 angles of one triangle are congruent to 2 angles
of another triangle, then the triangles are similar.
Given:
Conclusion:
ÐA @ ÐD
and
ÐB @ ÐE
DABC ~ DDEF
**MUST BE IN NOTES!**
SSS Similarity (Side-Side-Side)
If the measures of the corresponding sides of 2 triangles
are proportional, then the triangles are similar.
5
8
10
11
Given:
AB BC
AC
=
=
DE EF
DF
Conclusion:
16
22
8
11
5
=
=
16
22
10
DABC ~ DDEF
**MUST BE IN NOTES!**
10
SAS Similarity (Side-Angle-Side)
If the measures of 2 sides of a triangle are proportional to the
measures of 2 corresponding sides of another triangle and the
angles between them are congruent, then the triangles are
similar.
5
10
11
22
AB AC
Given: A  D and

DE DF
Conclusion:
DABC ~ DDEF
**MUST BE IN NOTES!**
Between or Within
Figure Comparisons


Between – each ratio made up of
corresponding sides of two different triangles
Within – each ratios made up of two sides of
one triangle
Right Triangle Ratios
Debrief: Right Triangles Similarity
 What
does it mean to use between-figure
ratios of corresponding sides of similar
triangles?
 What does it mean to use within-figure
ratios of corresponding sides of similar
triangles?
 How can within-figure ratios be used to
find unknown side lengths of similar
triangles?
Learning Target
DO NOW 12/10:
Are the two triangles similar?
I can …indirectly solve for
measurements involving right
triangles using scale factors,
ratios between similar
figures, and ratios within similar
figures.
Right Triangle
Similarity
Agenda
1. Note Card Similar Right
Triangles
2. Special Right Triangle
Ratios
3. Exit Ticket
Note Card: Similar Right
Triangles
 Draw
diagonal AB on your note card.
 Draw an altitude from one corner
perpendicular to the diagonal.
 Are
the triangles similar? How can we
know?
Creating Right Triangle Ratios
Exit Ticket
Learning Target
DO NOW 12/11:
Find the measure of x.
I can understand that the altitude
of a right triangle (from the vertex
of the right angle to the
hypotenuse) divides the triangle
into two similar right triangles that
are also similar to the original right
triangle.
Special Similar
Right Triangles
Agenda
1. Complete Packets
2. Embedded Assessment
3. Debrief
Debrief: Similar Right Triangles
 What
is an altitude, and what happens
when an altitude is drawn from the right
angle of a right triangle?
 What is the relationship between the
original right triangle and the two similar
sub-triangles?
 Explain how to use the ratios of the similar
right triangles to determine the unknown
lengths of a triangle.