ΔDEF
Figures that have the Same Shape BUT Different Sizes are considered to be Similar. In other words, if 2-polygons have Different Size Sides AND the Same Size Angles in the Same Exact Order going around the polygon ( either clockwise or counter-clockwise ), then the 2-polygons are Similar.
Corresponding sides and corresponding angles of similar polygons are identified in the same way that congruent polygons are identified using the vertices as the name of the polygon in corresponding order.
| Congruent Triangles: ΔABC
ΔDEF |
Similar Triangles: ΔABC ~ ΔDEF | ||
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A ratio is a comparison of two values by division. The ratio of two quantities, a and b, can be written in three ways:
A statement that two ratios are equal is called a proportion.
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In similar polygons the corresponding angles are congruent, but what about the corresponding sides of similar polygons? In similar polygons the corresponding sides are proportional by a Ratio of Similitude = k. The Ratio of Similitude "k", in similar polygons "k" is a value where by a side of one triangle is multiplied by "k" to equal the value of the corresponding side on the similar polygon.
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If two angles of one triangle are congruent to two angles of
another triangle, then the triangles are similar.
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| By.AA Triangle Similarity Theorem, ΔABC ~ ΔDEF. Find the Ratio of Similitude "k" from ΔABC to ΔDEF and the Ratio of Similitude "k" from ΔDEF to ΔABC. |
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Watch the video: |
Solution: |
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If two sides of one triangle are proportional to two
sides of another triangle and the included angles are congruent,
then the triangles are similar. |
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Given ΔABC & ΔDEF on the right. If ΔABC & ΔDEF are
similar by the SAS Triangle Similarity Theorem, find the measure of
DF. |
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Watch the video: |
Solution: | ||
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If the lengths of the sides of a triangle are proportional to
the lengths of the sides of another triangle, then the triangles
are similar. |
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Given ΔABC & ΔDEF on the right, determine if ΔABC & ΔDEF are
similar by using the SSS Triangle Similarity Theorem . |
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Watch the video: |
Solution: | ||
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Quick Question: Find the Ratio of Similitude "k" Instructions:
To use the app:
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Solve for the unknown side lengths in the similar figures
A.  |
B. |
C. |
D. |
1-10. Use the Quick Question:
Find
the Ratio of Similitude
"k" to do 10-Random problems.
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11-20. Use the Quick Question:
Find the Missing Side Measure
to do 10-Random problems.
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21-30. Use the Quick Question:
Are the Triangles Similar?
to do 10-Random problems.
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31. If the polygons ABCD and EFGH are similar, what are the values of
x, y, and z? |
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32. If the quadrilaterals at right are similar, what is m E
and the length of XY ?
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33. On a sunny day, a tall tree casts a shadow 26 ft long. A four
and a half foot tall child is standing near the tree and casts a shadow 18 inches long. To the nearest yard, how tall is the tree? Draw out the situation! |
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to
begin, click
for full screen mode
to
check your answer.
to goto the next problem 
to stop the app