By: Lazar Trifunovic and Jack Bloomfeld

• A ratio is a number of a certain unit divided by a number of the same unit.

• A proportion is an equation that equates two ratios

• Properties of Proportions:1. Cross product property

if a/b = c/d then ad=bc2. Reciprocal property

if two ratios are equal, then their reciprocals are also equal.

Jake was able to complete 12 math problems in 6 minutes. He wants to know how long it would take him to complete 30 problems at the same rate. How many minutes would it take?

12/6=30/x

X=????

The geometric mean of two positive numbers is the square root of the product of the two numbers.

Additional properties of proportions:If A/B=C/D then A/C=B/DIf A/B=C/D then (A+B)/B=(C+D)/D

Hunter is trying to create similar triangle for a math project.

Hunter has figured out thatdb/ad=ec/aewhat could he do to prove thatab/ad=ac/ae?

a

b c

d e

When the corresponding angles of two polygons are congruent and the lengths of corresponding sides are proportional the two polygons are similar.

Theorem 8.1If two polygons are similar then the ratio of

their perimeters is equal to the ratios of their corresponding sides.

• Cooper has a model of a hexagonal fence for his dog.

• Each angle of the model is 60 degrees.If he wants the modelto be similar to the fencehe’s building, how manydegrees will each angle ofthe real fence be?

model

Postulate 25, Angle-Angle similarity postulateIf two angles of one triangle are congruent to

the two corresponding angles of another triangle then the two triangles are similar.

You need to check if two right triangles are similar for geometry class. What is the fewest number of angles you need to measure to prove that the two triangles are either similar or not similar?

Theorem 8.2 SSS Similarity Theorem.If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Theorem 8.3 SAS similarity TheoremIf an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.

Jack’s pyraminxs look alike to him. Are they similar?

32 32

24

4 4

6

Theorem 8.4 Triangle Proportionality TheoremIf a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

Theorem 8.5 Converse if TPTIf a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Theorem 8.6If three parallel lines intersect two transversals then they divide the transversals proportionally.

Theorem 8.7If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the other two sides.

Fred has a triangle garden and he added a fence around the garden and also another fence in the garden to separate fruits from vegetables. The fence divides the two sides of the triangle proportionally. What do we know about the garden?

A

BC

ED

The dilation is a reduction or enlargement. Shaggy wants to make his second rectangular garage 3 times bigger. What are the new side measures and what is the scale factor.

4

5

L

W