Unit 7 Similarity

Part 1 Ratio / Proportion

A ratio is a comparison of two quantities by division. – You can write a ratio of two numbers a and b, where b≠0 three ways a:b, a to b or When expressing a ratio in simplest form they must be the same units of measure

Example A bonsai tree is 18 in. wide and stands 2 ft tall. What is the ratio of the width of the tree to the height of the tree?

Example 2 The measure of two supplementary angles are in the ratio 1:4. What are the measures of the two angles? – Since ratio’s are just reduced fractions we need to find the value by which they were reduced, x. So our two angles are 36 and 144, notice 36:144 reduces to 1:4

Extended Ratio An extended ration compares three or more numbers Example: The length of the side a triangle in the extended ratio 3:5:6. The perimeter of the triangle is 98 in. Find the length of the longest side. The longest side is 42 inch.

Example 2 The ratio of the sides of a triangle is 7: 9: 12. The perimeter of the triangle is 84 inch. Find the length of each side. – x = 3, 21, 27, 36 The ratio of the angles of a triangle is 5: 7: 8, find the measure of each angle. – x = 9, 45, 63, 72

Proportion – an equation that states two ratios are equal The first and last numbers if the proportion are the extremes and the two middle numbers are the means. Cross Product – When solving a proportion you multiply the extremes and set them equal to the means – Example: ay = xb

Examples

Properties of Proportions Is equivalent to

Part 2 Similar Polygons

Similar Polygons (6.2) Similar Polygons are polygons that have the same shape but may be different in size. Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional!

Scale Factor When comparing the length of corresponding sides you will get a numerical ratio. This is called the scale factor. – They are often given for models of real life objects. (Tell you how much larger or smaller and object is)

Example