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Welcome to Unit 3! Tear out page 271 and return your SB book. U3H4: Pg. 271 #1-­‐8 What to Study: Dilation, scale factor, similar, similarity statement, similarity ratio, SSS, AA, and SAS Similarity Theorem. Updates: U3Q1 (Activity 17 through 18-­‐2) 1st/4th/6th will be Monday, November 16th Agenda (1) Classroom Reminders (2) Warm-­‐Up! (3) Review U3H3 (4) Activity 18 (5) Tarzan Prompt (6) Cool-­‐Down Reminder – Unit 2 Test must be taken by November 16th (this Monday!) Classroom Reminders I have noticed a lot of bad manors in this class and in tutorial lately… Please have this in mind: Keep it Classy, Keep it *Clean*, Keep it Collaborative . Warm-­‐Up! Take 3 minutes to review the vocabulary we have learned so far… I am going to call on random students to tell me their deZinition without using their notes. J U3H3: Worksheet #’s 4-­‐6, 9-­‐11, 19-­‐20, 24 I will show you solutions under the document camera. Learning Objectives Students will be able to: Ø Develop criteria for triangle similarity. Ø Use similar triangles to solve word problems. Similarity and Proportions Ø Recall, what are the 5 Triangle Congruence Criteria? What are the two Non-­‐Congruence Criteria? Ø Recall, to be similar what must be true? As a group rearrange the given triangles into groups of similar triangles. Ø Visually, how do you know each group of triangles are similar? Similarity and Proportions Ø Which Congruence Criteria might be used to show that two triangles are similar? (Hint: there are three) There are three ways to prove triangles are similar: (1)  SSS (2)  AA (3)  SAS Similarity and Proportions Title the right side of your notebook: U3A18 Similarity and Proportions (30) Similarity and Proportions Side-­‐Side-­‐Side (SSS) Similarity Theorem o  If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar. •  http://www.mathopenref.com/similarsss.html Similarity and Proportions Angle-­‐Angle (AA) Similarity Theorem o  If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Table – Talk: q  Why do you think we only need two congruent angles (AA) instead of all three angles to prove similarity? –  http://www.mathopenref.com/similaraaa.html Similarity and Proportions Side-­‐Angle-­‐Side (SAS) Similarity Theorem o  If two sides of one triangle are proportional to two sides of another triangle and the angle between the sides are congruent, then the triangles are similar. •  http://www.mathopenref.com/similarsas.html Similarity and Proportions =
=
3
5
1
2
Similarity and Proportions ratios are not all the same, the triangles are not similar.
ary
ngles are similar if all their corresponding angles are congruent (exactly the same) and their corresponding
proportional (in the same ratio).
Practice
e if any of the
triangles below are similar. Compare two triangles at a time.
(e)$Determine$if$any$of$the$triangles$below$are$similar.$Compare$two$triangles$at$a$time.$$
$
$
$
$
$
$
$
BC ⇠ 4DEF?
$
EF ⇠ 4GHI?
$
BC ⇠ 4GHI?
$
:
$
22
24
and 4DEF: Is 20
15 = 16 = 18 ?
$
4 22
11
24
4
ach fraction to see if they are equal. 20
15 = 3 , 16 = 8 , and 18 = 3 .
$
4ABC and 4DEF are not similar.
F and 4GHI: Is
6
3
2
3
=
16
33 ,
and
18
36
= 12 .
=
1
2
16
33
=
18
36 ?
16
33 , 4DEF
22
24
33 = 36 ?
6=
20
30 =
24
2
36 = 3 . All
and 4GHI: Is
= 23 , and
15
30
is not similar to 4GHI.
three ratios reduce to 23 , 4ABC ⇠ 4GIH.
Similarity and Proportions Before reviewing the solutions as a class it is always good to ask your peers. We are going to Zind other partners and compare solutions. If you think your partner is incorrect then have a conversation on why you are right or maybe why you are wrong. Find another person in the room with the same hair color as you. Sit next to them and compare solutions. Find a different person in the room with the same shirt color as you. Sit next to them and compare solutions. Similarity and Proportions Sometimes in math we cover concepts and are unsure of how we can actually use it in the real world. Well FINALLY here are some examples of similarity. J Thales is known as the Zirst Greek scientist, engineer, and mathematician. Legend says that he was the Zirst to determine the height of the pyramids in Egypt! He did this by examining the shadows made by the Sun. He considered three points: the top of the pyramids, the lengths of the shadows, and the bases. In your Tables, discuss the following questions. (1) What appears to be true about the corresponding angles in the two triangles? (2) If the corresponding sides are proportional, what could you conclude about the triangles? Similarity and Proportions Indirect Measurement o  Any method that uses formulas, similar Zigures, and/or proportions to measure an object. o  Thales used indirect measurement to measure his height and the length of his shadow and compared it with the length of the shadow cast by the pyramid to Zind the height of the pyramid. Whiteboards! If the person is 5ft tall, his shadow is 7 ft long, and the length of the pyramids’ shadow is 100 ft long, how tall is the pyramid? Similarity and Proportions In reality, we are not all going to be measured to the nearest ft. For example, I am 5 foot 3 inches. Let’s do (1a). Similarity and Proportions Scale Drawing o  Represents an object as smaller than or larger than its actual size. The drawing’s scale is the ratio of any length in the drawing to the corresponding actual length. o  For example, on a map with a scale of 1 cm : 1500 m, one centimeter on the map represents 1500 m in actual distance. Similarity and Proportions Tarzan Prompt The last problem on your guided notes is the Tarzan Prompt. Take 5 minutes to complete. We are going to temporarily switch seats and compare solutions for the prompt. Cool-­‐Down… Please put your name and period on a half sheet of binder paper. •  Create your own word problem that involves one of the following: o  Indirect Measurement o  Scale Drawing •  Solve your word problem. •  If I like your word problem I could possibly use it for the quiz on Monday. Review U3H1 Any mistakes you made on this homework please ask for clariZication if you are still confused J