Monday 1/5 Similarity Ch.11 Textbook p. 564 one inside table
Use patty paper to complete step 1. Use the ruler on your
protractor to complete step 2. In five minutes, you will be quizzed
for credit.
Slide 4
Quiz Question 1 Whiteboard, marker & rag in table. Hold up
answer, facing forward, 1 min. Q: Are these shapes congruent?
A.Yes, they have the same angles. B.Yes, they can be superimposed.
C.No, they have the same angles but not the same sides. D.Cannot be
determined. (CBD)
Slide 5
Polygons are similar if, Their corresponding angles are
congruent (same) and, Their corresponding sides are proportional.
All the corresponding pairs of sides have the same ratio.
Slide 6
Calculate the ratio of each pair of corresponding sides in
these shapes. Record on patty paper. Example: RS/CD = 4.1/2.3 = 1.8
In five minutes, you will be quizzed for credit.
Slide 7
Quiz Question 2 (1 min) Whiteboard, marker & rag in table.
Hold up answer, facing forward. Q: Are these shapes similar? A.Yes,
they have the same angles and side ratios. B.Yes, they can be
superimposed. C.No, they have the same angles but not the same
sides. D.Cannot be determined. (CBD)
Slide 8
Notes Date TitleSimilarity & Dilations Ch. 11
Slide 9
Polygons are similar if, Their corresponding angles are
congruent (same) and, Their corresponding sides are proportional.
All the corresponding pairs of sides have the same ratio.
Slide 10
Dilation Process of growing Example: Eye pupils dilate in dark.
Scale factor How much the pre- image has grown to create the image.
Example: 3:1 = scale factor 3 Calculate scale factor by dividing
length of corresponding sides image/pre-image.
Slide 11
Pre-image 3 cm -> Image 9 cm = 9/3 = scale factor 3
Pre-image 8 cm -> Image 2 cm = 2/8 = scale factor = 0.25 Scale
factor > 1 is growing Scale factor < 1 is shrinking
Slide 12
Quiz Question 3 (1 minute) Q: Are these shapes, A.Congruent
B.Similar C.Congruent & Similar D.Neither
Slide 13
Are corresponding angles congruent? YES. (90 o ) Are
corresponding sides proportional? NO. Conclusion These polygons are
not similar or congruent.
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Quiz Question 4 Answer # 1, p. 568 on whiteboard.
Slide 15
Quiz Question 5 Answer # 8, p. 568 on whiteboard.
Slide 16
Quiz Question 6 Answer # 5, p. 568 on whiteboard. Also write
the scale factor.
Slide 17
Cleanup Grade Start at 100% each quarter. Lose credit if dont:
Push in chair to touch table. Pick up trash near desk, even if not
yours. Remove trash inside desk. Erase whiteboard. Return textbook,
whiteboard, marker, rag into desk. Also start with 100% for
following rules
Slide 18
HW p. 568 # 1-10 # 1 & 2 Find two shapes that have same
angles and corresponding parts, but have different sizes. # 3 5
Draw original shape on graph paper. Then repeat but make all sides
bigger by same amount. (2x?)
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Slide 20
Have HW open in first minute of class to earn credit. Open
textbook to p. 568. Tuesday 1/6 Similarity Ch.11
Slide 21
1.You will be quizzed for credit on this in 10 min. 2.Place a
point on the left of a new page in your notebook. 3.Draw three rays
radiating out from this point, to the upper, middle & lower
right. 4.Randomly place an additional point on each ray. Connect
them to form a triangle. 5.Place a second point on each ray, at
twice the distance as the first. Connect to make a second triangle.
6.What do we notice about the two triangles?
Slide 22
Quiz Question 1 (1 minute) Q: What is the relationship between
these triangles? A.Congruent B.Similar C.Congruent & Similar
D.Neither
Slide 23
Quiz Question 2 (1 minute) Q: What is the scale factor? A.0.5
B.1.0 C.2.0 D.None of the above
Slide 24
Quiz Question 3 (1 minute) Q: Corresponding sides in these two
triangles are: A.congruent B.parallel C.perpendicular D.None of the
above
Slide 25
Dilations Centered on Same Point
Slide 26
Dilations work for all polygons Center of dilation can be
inside shapes. Scale factor can be negative What is the scale
factor in this dilation?
Slide 27
Similar Shapes Centered on Same Point of Dilation...
Corresponding angles are congruent (same.) Parallel corresponding
sides. Ratios of every pair of corresponding sides is the same.
Ratios of center-to-vertex distances are the same for corresponding
vertices in each shape. Ratios between sides in the same shape, are
the same in both shapes.
Slide 28
Slide 29
You will be quizzed on the following graph in 10 minutes. On
your personal whiteboard graph: (3,2) (4, -2) (-2, -3) Dilate
triangle with scale factor of 2, Draw rays centered on origin.
Write a coordinate rule for this. Wednesday 1/7 Similarity
Ch.11
Slide 30
Dilation Centered on Origin
Slide 31
Coordinate rules for dilations 2x dilation:(x, y) (2x, 2y) 3x
dilation:(x, y) (3x, 3y) Stretch - shapes not similar! (x, y) (2x,
y) Another stretch: (x, y) (x, 2y)
Slide 32
Are corresponding angles congruent? YES. (90 o ) Are
corresponding sides proportional? NO. Conclusion These polygons are
not similar or congruent. If all corresponding angles remain
congruent, must sides be proportional?
Slide 33
If all sides are proportional, must corresponding angles remain
congruent? Scale factor consistently 18/12=1.5 Butare corresponding
angles congruent? NO!
Slide 34
How to Know if Shapes are Similar Corresponding angles
congruent? YES. Corresponding sides proportional? YES. Conclusion
These polygons are similar. CORN ~ PEAS
Slide 35
AA Triangle Similarity Shortcut However, if two angles in a
triangle are the same
Slide 36
AA Triangle Similarity Shortcut However, if two corresponding
angles in two triangles are the samethen both triangles must be
similar! Do not need to measure third pair of angles (Triangle Sum
Conjecture says they must be the same.) Do not need to measure
sides or calculate scale factor sides must all grow/shrink by same
ratio to keep angles congruent.
Slide 37
HW p. 574 # 1-10
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Slide 39
Have HW open in first minute of class to earn credit. Open
textbook to p. 574 Thursday 1/8 Similarity Ch.11
Slide 40
Measuring Height w Similar Triangles
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Slide 42
Measuring Height or Distance with Similar Triangles
Slide 43
Measuring Height w Similar Triangles
Slide 44
Slide 45
Highest edge of U.S. flag in commons Gold ball on flagpole in
front of school Water tower (extra credit) Measure two ways each:
mirror & ruler Each partner records data & calculations You
will be quizzed on your answers & methods next week. Friday 1/9
Measure Heights of Tall Objects with Similar Triangles
Slide 46
Mirror Ruler Friday 1/9 Measure Heights of Tall Objects with
Similar Triangles
Slide 47
Place mirror, meter stick, little ruler on desk to be checked
in.
Slide 48
Slide 49
Continue to measure: Highest edge of U.S. flag in commons Gold
ball on flagpole in front of school Water tower (extra credit)
Measure two ways each: mirror & ruler Each partner records data
& calculations You will be quizzed on your answers &
methods next week. Monday 1/12 Measure Heights of Tall Objects with
Similar Triangles
Slide 50
Place mirror, meter stick, little ruler on desk to be checked
in.
Slide 51
HW HW due tomorrow 11.3 #1-10. Quiz tomorrow, sections 1-3. May
use your notes. May NOT use cell phone calculator for scale
factors.
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Slide 53
Have HW open in first minute of class to earn credit. Have
textbook open to p. 582. Tuesday 1/13 Similarity Ch.11
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14.0 cm on Google Maps 4.0 cm on Google Maps
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Slide 56
Wednesday 1/14 QUIZ May use notes & calculator. No cell
phones.
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Slide 58
Thursday 1/15 Review for Test 1.In notebook, graph (3, 2) (4,
-1) (-3, 3) (-2, -5). Tape in graph paper if needed. 2.Draw rays
from origin through each vertex. 3.Dilate above shape with scale
factors of 0.5 and 2. 4.Write as complete sentences: In a dilation,
_________ angles ___________. We can control the scale factor by
_____________________________________.
Slide 59
Dilation using ray method
Slide 60
Thursday 1/15 Review for Test 1.In notebook, graph (3, 2) (4,
-1) (-3, 3) (-2, -5). Tape in graph paper if needed. 2.Draw rays
from origin through each vertex. 3.Dilate above shape with scale
factors of 0.5 and 2. 4.Write as complete sentences: In a dilation,
corresponding angles remain congruent. We can control the scale
factor by increasing the distance between center-of-dilation &
vertices by that factor.
Slide 61
Dilations Centered on Same Point Dilations work for all
polygons Center of dilation can be inside shapes. Center of
dilation can be outside shapes.
Slide 62
Dilations Centered on Same Point Scale factor can be negative
What is the scale factor in this dilation?
Slide 63
1.Compare polygon (3, 2) (4, -1) (-3, 3) (-2, -5) and polygon
(5, 0) (6, -3) (-1, 1) (0, -7). 2.Write as complete sentence: These
polygons are: congruent/similar/neither (may be more than one)
because __________ _____________________. 3. If similar, the scale
factor is ____________.
Slide 64
1.Compare polygon (3, 2) (4, -1) (-3, 3) (-2, -5) and polygon
(1.5, 2) (2, -1) (-1.5, 3) (-1, -5). 2.Write as complete sentence:
These polygons are: congruent/similar/neither (chose one) because
_____________________. 3. If similar, the scale factor is
____________.
Slide 65
1.Compare polygon (3, 2) (4, -1) (-3, 3) (-2, -5) and polygon
(1.5,1) (2,-0.5) (-1.5,1.5) (-1,-2.5). 2.Write as complete
sentence: These polygons are: congruent/similar/neither (chose one)
because _____________________. 3. If similar, the scale factor is
____________.
Slide 66
Slide 67
Friday 1/16 30 min No notes No cell phone Yes calculator 10/10
= A+ 9/10 = A- 7/10 = B 5/10 = C 3/10 = D TEST Similarity &
Dilations
Slide 68
Slide 69
A level topics 11.4 & 11.5 Verify geometric properties of
dilations
Slide 70
WarmUp 5 min Draw a square 2 cm on each side. Draw a square 6
cm on each side. Draw dashed lines to show how many little squares
fit in the big square. Calculate the area of each and write in each
square with units. Fill in this Conjecture: If corresponding sides
of two similar polygons compare in a ratio of m/n, then their areas
compare in the ratio of ______________.
Slide 71
Proportional Volume Conjecture Draw a cube 2 cm on each side.
Draw a bigger cube 6 cm on each side. Draw dashed lines to show one
little cube in the corner of the big cube. Calculate the volume of
each cube. Fill in this Conjecture: If corresponding edges (or
radii or heights) of two similar solids compare in a ratio of m/n,
then their volumes compare in the ratio of ______________.
Slide 72
For shapes with a scale factor of 2, how do these scale up?
Perimeter? Area? For solids with scale factor of 2, how do these
scale up? Surface Area? Volume?
Slide 73
For shapes with a scale factor of 3, how do these scale up?
Perimeter? Area? For solids with scale factor of 3, how do these
scale up? Surface Area? Volume?
Slide 74
Worksheet to Complete Lesson 11.5 Proportions with Area and
Volume
Slide 75
1) Which two HW Qs would you most like to see? 2) Working with
your partner, read pp. 599-602 Why Do Elephants Have Big Ears?
Discuss, then write your answers for Qs 1-15. Show Mr. Sidman.
Slide 76
1.You will need your compass. 2.Place a point in the center of
the notebook page. 3.Draw three rays radiating out from this point.
4.Randomly place one additional point on each ray. Place them at
the edges of the paper. Connect them to form a BIG triangle.
5.Place a second point at half the distance along each ray as the
first. This makes a similar triangle with a scale factor of 0.5
compared to the first. 6.Bisect one corresponding side of each
triangle. 7.Construct one corresponding median for each triangle.
Find the ratio of big-to-little medians. 8.Bisect a corresponding
angle in each. Find the ratio of the big-to-little angle bisector
segments.
Slide 77
Conclusion Corresponding (matching) dimensions of similar
triangles all have the same scale factor (ratio): little side =
little median = little angle bisector big side big median angle
bisector little altitude = little midsegment = little perpendicular
bisector big altitude big midsegment big perpendicular
bisector
Slide 78
1.You will need your compass. 2.Place a point in the center of
the notebook page. 3.Draw three rays radiating out from this point.
4.Randomly place one additional point on each ray. Place them at
the edges of the paper. Connect them to form a BIG triangle.
5.Place a second point at half the distance along each ray as the
first. This makes a similar triangle with a scale factor of 0.5
compared to the first. 6.Find the ratio of the small-to-big
perimeters. 7.For one corresponding angle in each triangle, drop a
perpendicular bisector to the opposite side. 8.Use this altitude
(height) to find the ratio of areas.
Slide 79
WarmUp 5 min 1.Write a step-by-step proof that LMN EMO. 2.What
is length y?
Slide 80
1.Draw two rays forming an acute angle. 2.On one ray, use a
ruler to mark off lengths 8 cm and then an additional 10 cm from
vertex. Label these segments. 3.On the other ray, mark off segments
12 cm and an additional 15cm. 4.Connect points to make a little
triangle inside the big. 5.Are these triangles similar? 6.Calculate
the ratio 8cm to 10cm. 12cm to 15cm. What do you notice? 7.What
else do you notice about these triangles?
