4.6

How Can I Organize My Information?

Pg. 19Creating a Longer Flowchart

4.6–How Can I Organize My Info?Creating a longer flowchart

In Lesson 4.5, you developed the AA~ and SSS~ conjectures to help confirm that triangles are similar. Today you will continue working with similarity and will learn how to use flowcharts to organize your reasoning.

4.30 – FLOWCHARTS Examine the triangles at right. 

a. Are these triangles similar? Use full sentences to explain your reasoning.

Yes, AA~

b. Julio decided to use a diagram (called a flowchart) to explain his reasoning. Compare your explanation to Julio's flowchart. Did Julio use the same reasoning you used?

c. What appears to go in the bubbles of a flowchart? What goes outside the bubbles?

Inside:Statements

Outside:Reasons

4.31 – WRITING FLOWCHARTS Besides showing your reasoning, a flowchart can be used to organize your work as you determine whether or not triangles are similar.  a. Are these triangles similar? Why?

Yes,

SSS~

b. What facts must you know to use the triangle similarity conjecture you chose? Julio started to list the facts in a flowchart at right. Complete the third oval.

164

4

given

c. Once you have the needed facts in place, you can conclude that you have similar triangles. Add to your flowchart by making an oval and filling in your conclusion.

given

164

4

~CDF RTQ ~SSS

d. Finally, draw arrows to show the flow of the facts that lead to your conclusion and record the similarity conjecture you used, following Julio's example.

given

164

4

~CDF RTQ ~SSS

4.32 –FLOWCHART ARROWS Lindsay was solving a math problem and drew the flowchart: a. Draw and label two triangles that could represent Lindsay's problem. What question did the problem ask her? How can you tell?

AR

B Q

CS

Prove the triangles are similar

b. Lindsay's teammate was working on the same problem and made a mistake in his flowchart. How is this flowchart different from Lindsay's? Why is this the wrong way to explain the reasoning in Lindsay's problem?

Arrows go the wrong way

4.33 – HOW MANY OVALS?Ramon is examining the triangles at right. He suspects they may be similar by SSS~.

a. Why is SSS~ the best conjecture to test for these triangles?

Only know sides

b. Set up ovals for the facts you need to know to show that the triangles are similar. Complete any necessary calculations and fill in the ovals.

1612

= 43

2418

= 43

= 54

2016

given given given

c. Are the triangles similar? If so, complete your flowchart, using an appropriate similarity statement. If not, explain how you know.

Not similar 43

= 54

4.34 – START FROM SCRATCH Now examine the triangles at right. a. Are these triangles similar? Justify your conclusion using a flowchart.

46

=23

8 12

= 23 = 2

31015

ΔTAC ~ ΔIGP

SSS~

given given given

b. What is How do you know??m C

22.3m C Similar shapes have corresponding angles =

4.35 – EXTRA INFORMATION NEEDEDDetermine if you can prove the triangles are similar by AA~ or SSS~. What information are you given? Do you need to find more information to determine if the triangles are similar? What extra information do you need in order to prove these are congruent? Find the missing information and complete the flowchart that uses the given information to state what else we know about the triangles to prove them similar.

b. Set up ovals for the facts you need to know to show that the triangles are similar. Complete any necessary calculations and fill in the ovals.

RT//QU

SRT SQU

Corresponding angles

S S Reflexive

~RST QSU AA~

x2 + 162 = 202

x2 + 256 = 400x2 = 144x = 12

12

129

= 43

Pyth. thm

1612

= 43

2015

= 43

SSS~

IGH ~ JKL

Vertical angles are =

SRT PRQ

IHIH

= 1

Reflexive Prop

DID ALREADY!!!!!!!!!!

W V Alternate interior angles

XYW ZYV

Vertical angles

Straight angle28°

ABE DBC A D

Triangle Sum