wednesday, september 25 th
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Wednesday, September 25 th. Warm Up. S is the centroid. If MS=12, what is SP? If NQ=18, what is SQ?. Today’s Goal. Identify similar polygons. Apply properties of similar polygons to solve problems. Which shapes are similar and how do you know?. 1. 3. 2. - PowerPoint PPT PresentationTRANSCRIPT
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Wednesday, September 25th
S is the centroid. 1. If MS=12, what is SP?2. If NQ=18, what is SQ?
Warm Up
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Identify similar polygons.
Apply properties of similar polygons to solve problems.
Today’s Goal
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Which shapes are similar and how do you know?
1.
2. 3.
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Figures that are similar (~) have the same shape but not necessarily the
same size.
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Remember-Congruent
Have the same size
and shape
EXACTALY THE
SAME!!!!!
Represented by:
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Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.
Definition
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Similar FiguresTwo figures are similar if• the measures of the corresponding angles are equal• the ratios of the lengths of the corresponding sides are proportional
Similar figures have the same shape but not necessarily the same size.
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Finding missing angles
• Hint: Remember angles are the same in corresponding angles!
What is angle D? <D
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#1 Identify the pairs of congruent angles and corresponding sides
N Q and P R. By the Third Angles Theorem, M T.
0.5
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B G and C H. By the Third Angles Theorem, A J.
#2 Identify the pairs of congruent angles and corresponding sides
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A similarity ratio is the ratio of the lengths of
the corresponding sides of two similar polygons.
The similarity ratio of ∆ABC to ∆DEF is , or .
The similarity ratio of ∆DEF to ∆ABC is , or 2.
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Think: What am I multiplying or dividing all sides by to get
the lengths of the other triangle?
Also known as the SCALE FACTOR or DIALATION
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Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.
Writing Math
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#1 Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.
∆ABCD and ∆EFGH
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Step 1 Identify pairs of congruent angles.
P R and S W isos. ∆
Step 2 Compare corresponding angles.
Since no pairs of angles are congruent, the triangles are not similar.
mW = mS = 62°
mT = 180° – 2(62°) = 56°
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Step 1 Identify pairs of congruent angles.
#2 Determine if ∆JLM ~ ∆NPS. If so, write the similarity ratio and a similarity statement.
N M, L P, S J
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Step 2 Compare corresponding sides.
Thus the similarity ratio is , and ∆LMJ ~ ∆PNS.
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Finding Scale Factor Practice
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Ticket to Go: Textbook page 249
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