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Stretching and Shrinking
Topics
1. Similar Figures
Key Terms:
Similarity
Scale Drawings
Scale Factor
Corresponding Sides
Corresponding Angles
Supplementary Angels
Complementary Angles
Image
Scale Factor
Learning Targets:
1. Compare geometric figures for similarity and determine scale factors. (MS 7.3.2.1)
2. Determine side lengths (perimeter) and areas of similar figures. (MS 7.3.2.2)
3. Explain how a scale factor affects the perimeter and area of similar figures.
4. Use algebraic rules to produce similar figures
2. Ratios
Key Terms:
Equivalent representations (percents, decimals, fractions)
Equivalent fractions
Ratios
Scale Factor
Learning Targets:
1. Find missing sides lengths using ratios or scale factors
2. Compare two ratios of corresponding sides to determine if figures are similar (equivalent fractions) (MS
7.1.1.5)
3. Proportions
Key Terms:
Scale factor
Proportional
Equations
Learning Targets:
1. Use proportions to solve problems in various contexts. (MS 7.1.2.5)
2. Solve multi-step problems involving proportional reasoning. (MS 7.2.2.2)
3. Be able to explain how to solve a proportion using scale factors.
4. Use proportions and ratios to solve problems involving scale drawings. (MS 7.3.2.3)
5. Solve equations resulting from proportional relationships. (MS 7.2.4.2)
Stretching and Shrinking
Vocabulary Developed in Previous Units
congruent
fractal
midpoint
nested triangles
parallel
parallelogram
polygon
probability
quadrilateral
ratio
square
square root
tessellation
transformation
Vocabulary Developed in this Unit
Complementary angles Complementary angles are a pair of angles whose measures add to 90 degrees.
Corresponding Corresponding sides or angles have the same
relative position in similar figures. In this pair of similar
shapes, side AB corresponds to side HJ, and angle BCD
corresponds to angle JKF.
Equivalent ratios Ratios whose fraction representations are
equivalent are called equivalent ratios. For instance, the ratios
3 to 4 and 6 to 8 are equivalent because 3/4 = 6/8.
Image The figure that results from some transformation of a figure. It is often of interest to consider what is the
same and what is different about a figure and its image.
Midpoint A point that divides a line segment into two segments of equal length. In the figure below, M is the
midpoint of segment LN.
Nested triangles Triangles that share a common angle are sometimes
called nested. In the figure below, triangle ABC is nested in triangle
ADE.
Stretching and Shrinking
Ratio A ratio is a comparison of two quantities. It is sometimes expressed as a fraction. For example, suppose
length AB is 2 inches and length CD is 3 inches. The ratio of length AB to length CD is 2 to 3, or 2/3.The ratio
of length CD to length AB is 3 to 2, or 3/2.
Rep-tile A figure you can use to make a larger, similar
version of the original is called a rep-tile. The smaller
figure below is a rep-tile because you can use four copies
of it to make a larger, similar figure.
Scale factor The number used to multiply the lengths of a
figure to stretch or shrink it to a similar image. If we use a
scale factor of 3, all lengths in the image are 3 times as
long as the corresponding lengths in the original. When
you are given two similar figures, the scale factor is the
ratio of the image side length to the corresponding
original side length.
Similar Similar figures have corresponding angles of equal measure and the ratios of each pair of
corresponding sides are equivalent.
Supplementary angles Supplementary angles are two angles that form a straight line. The sum of the angles is
1808.