Journal Entry #9
During the past two weeks we have been investigating similar figures. For this journal entry you need to write about three things.
a) Explain the bullet points below in full sentences to give a background on similar figures.
· Explain what a ratio is and how they relate to proportions. Give an example of a ratio and a proportion. (7-1)
· Describe what the cross products are in a proportion. Give an example where you use cross products. (7-1)
· Explain the term “similar polygons”. Describe what is true about similar polygons. Give an example. (7-2)
· Explain what a scale factor is and how to calculate a scale factor. Give an example. (7-2)
· Describe the three ways to determine two triangles are similar. Sketch a picture to illustrate each. (7-3)
· Explain how triangles can be used in indirect measurements, especially by measuring a shadow of a tall object. (7-3)
b) Consider the problem below.
· Write a similarity statement comparing the two triangles. Explain which property you can use to determine similarity. Note: if you do not know x you can not assume anything about the sides.
· Write a proportion to solve for x. Explain how you set up the proportion.
· Solve for x and the measure of the unknown sides. Explain your math in full sentences.
c) Write a reflection on the problem above and how you feel about similar figures in general.
· A ratio is a comparison of two numbers you can separate the 2 number in the ratio with a colon or as a fraction. A proportion is an equation with a ratio on each side. If is a statement that two ratio on each side. If is a statement that two ratios are equal.
Example: ,
· You cross multiply to test where two ratios are equal and a form a proportion. You multiply the outer terms called extremes and the middle terms called the means.
Example: 20*5=100 100=100
You can also use cross to find a missing term in the proportion
Example: = x=75
· Similar polygons are the same shape, same angles, but different sides.
7 3
· A scale factor is the ratio of the lengths of two corresponding sides of two similar polygons
· Three ways to determine two triangles are similar is by using AA,SSS,SAS.
AA-angle angle means that the triangles have two of their angles equal. If so the triangles are similar.
SAS- side angle side means the ratio between another two sides and we know the included angles are equal.
SSS-side side side means we have the two triangles with all three partial ponding sides in the same ratio
· Indirect measurements allows you to use properties of similar polygons
10x+60=16x +24
-10 -10
60=6x+24
-24 -24
· Setting up the proportions I set up the 10 over 8because both sides are similar and 2x+3 over x+6 because they are that same as well. Then I cross multiplied I got 10x+60=16x+24 im solving for x so I need to set together the lite terms
C) This journal entry was pretty easy I had difficulties with problem B because I got two answer -14 and 6 so I don’t know, but other than that everything was straight forward Also the indirect measurements im not really familiar with it.
