SIMILARITY
MATH 8
Similar Polygons
polygons that have corresponding angles that are congruent and
corresponding side lengths that are proportional
when a dilation occurs the polygons are similar
Similarity Statements
- statements showing the similarity between sides in different shapes
- similarity symbol is
Statement of Proportionality
- statement showing the equality of the ratio (scale factor) between all corresponding sides on similar polygons
- written as fraction equations, proportions can be solved for unknown measures
Determine whether the figures are similar or not. Explain
10
7
6
3
Not similar, the sides are not proportional
7
14
4
8
10
20
Similar, the sides are proportional
same shape
same shape
The following figures are similar. Write the similarity statements for each set of similar figures. List all pairs of congruent angles and write the statements of proportionality for all corresponding sides.
Angles
Sides
Statements of Proportionality
Proportion Review: Find the value of x
Cross-products
must be equal
Use the similar figures to find the missing measures
WZ = 19.5
AB
Statements of Proportionality
WZ
AB = 16
Select a pair of corresponding sides where both values are known
Scale Factor
used to dilate a polygon, can be used as half a proportion to solve for unknown measure
Some of the fastest land-speed records by cars have been set at Utah’s Bonneville Salt Flats. In one of the vehicles, the ratio of the model car designed to the actual car built is 5:34. If the axle of the model car was 8 inches, how long was the axle in the actual car?
A fire hydrant 2.5 feet high casts a 5-foot shadow. How tall is a street light that casts a 26-foot shadow at the same time? Let h represent the height of the street light.
Shadows form Similar Triangles
Mary is standing next to the flag pole outside the school. She uses a mirror to help her calculate the height of the flag pole. Mary is 5.5 feet tall and she is standing 2 feet from the mirror. The mirror was placed 11 feet from the base of the flagpole. What is the height of the flagpole?
Find the distance from the house to the traffic light.
What specific transformations would take Figure 1 to become Figure 2?
Translation (to move point A to overlap Point I)
Dilation (use I as center)
What specific transformations would take Figure 1 to become Figure 2?
Dilation (use A as center)
Translation