Similarity - Class Practice
A skate park is 24 yards wide by 48 yards long. If we used scale of 1 inch = 32 yards, what is the width and length of the scale drawing?
0.75 yards wide by 1.5 yards long
Find the Scale Factor: 10 cm = 5 m
1 cm = 50 cm
An area rug is 9 feet wide. In a photograph, the image of the rug is 3 inches wide. What is the scale?
1 inch = 3 feet
An architect is using a scale of 1 in. = 10 ft. What is this scale as a fraction?
10 ft. /1 in.
The record for the most amount of rain in the shortest period of time in the United States was 12 inches in 42 minutes. At this rate, how much rain would fall in 15 minutes?
4.29 inches would fall in 15 minutes
A five foot parking meter casts a 6 foot long shadow. At the same time of day, how long is the shadow of a nearby 80 for building?
96 foot long shadow
Extended Ratio
A comparison of three or more quantities written as a:b:c or a to b to c.
Ratio
A comparison of two or more quantities written as a/b, a:b, or a to b.
Scale Drawings
A drawing that shows a real object with accurate proportions reduced or enlarged by a certain amount.
Similarity Statement
A statement that matches the corresponding angles and sides from one figure to another.
Proportion
An equation stating that two ratios are equal.
What is a proportion?
An equation stating that two ratios are equal.
Triangle ABC is similar to triangle DEF. If the measure of angle A is 52 degrees and the measure of angle E is 67 degrees, what is the measure of angle C?
Angles A and D are both 52 degrees. Angles B and E are both 67 degrees. We can find the measures of both angles C and F by adding 52 + 67 = 119. Subtract 180 - 119 = 61 degrees.
What is the difference between congruent figures and similar figures.
Congruent figures are the exact same size and shape, but similar figures are the same shape but not necessarily the same size.
In order for two figures to be similar figures what two things have to be true about the two figures?
Corresponding angles are congruent and corresponding sides are proportional.
What do we know about the corresponding ANGLES of similar figures?
Corresponding angles of similar figures are CONGRUENT.
What do we know about the corresponding SIDES of similar figures?
Corresponding sides of similar figures are PROPORTIONAL.
Similar Polygons
Figures that are the same shape but different sizes because all of their corresponding angles are congruent and all of their corresponding sides are proportional. These figures also have perimeters that are proportional.
Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides into segments of proportional length.
Side Side Side Similarity (SSS)
If all three pairs of corresponding sides are proportional, then the triangles are similar.
Proportional Parts and Parallel Lines
If three or more parallel lines intersect two transversals, then they cut the transversals proportionally.
Angle Angle Similarity (AA)
If two pairs of corresponding angles are congruent, then the triangles are similar.
Side Angle Side Similarity (SAS)
If two pairs of corresponding sides are proportional AND their included angles are congruent, then the triangles are similar.
Converse of the Triangle Proportionality Theorem
If two sides of a triangle are segments of proportional length, then the line that divides them is parallel to the third side of the triangle.
Triangle LMN is similar to triangle RST. What is the value of LN if RT is 9 inches, MN is 21 inches, and ST is 7 inches.
LN = 27 inches
__________ is a ratio of a given length on a scale drawing or model to the corresponding length on the actual object.
Scale
What is used to represent an object that is too large or too small to be drawn or built at actual size?
Scale drawing or scale model
When talking about a scale drawing or model, _____________ is determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object. How do we write this as a fraction?
Scale: (Actual measure) / (Drawing Measure)
How do you use proportions to find a missing side length in similar figures?
Set up an equation as shown. Solve for x by cross multiplying. You will get the equation 3x = 6. Divide both sides by 3 to get the final answer: x = 2.
___________ are two figures that have the same shape but not necessarily the same size.
Similar Figures
Similar Polygons
Similar polygons have the exact same shape but not necessarily the same size. The corresponding angles are congruent and the side lengths are proportional.
Suppose A Monument in Texas casts a shadow of 285 feet. At the same time, a nearby tourist, who is 5 feet tall casts a 2.5 foot shadow. How tall is the Monument?
The Monument is 570 feet tall.
Scale Factor
The ratio of corresponding sides. Order matters.
The height of an amusement park ride is 157.5 feet. If the ride's shadow is 60 feet long, how long will a person's shadow be if the person is 5.3 feet tall?
The shadow will be about 2 feet long.
When should we use indirect measurement?
When we need to find measurements that are too difficult to measure directly.