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Bellwork Determine whether the two triangles are similar Determine whether the two triangles are similar Set 1 Set 1 ΔABC: m A=90 o, m B=44 o ΔABC: m A=90 o, m B=44 o ΔDEF: m D=90 o, m F=46 o ΔDEF: m D=90 o, m F=46 o Set 2 Set 2 ΔABC: m A=132 o, m B=24 o ΔABC: m A=132 o, m B=24 o ΔDEF: m D=90 o, m F=24 o ΔDEF: m D=90 o, m F=24 o Solve for x Solve for x Sun-Yung Alice Chang is a Chinese-American woman who earned a Ph.D. in mathematics from the University of California, Berkley in 1974. In 1995 she won a prize for outstanding research in mathematics. She was born in the year whose sum of digits is 22 and where the units digit is twice the tens digit. What year was she born? Sun-Yung Alice Chang is a Chinese-American woman who earned a Ph.D. in mathematics from the University of California, Berkley in 1974. In 1995 she won a prize for outstanding research in mathematics. She was born in the year whose sum of digits is 22 and where the units digit is twice the tens digit. What year was she born? Clickers

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Bellwork Solution Determine whether the two triangles are similar Determine whether the two triangles are similar Set 1 Set 1 ΔABC: m A=90 o, m B=44 o ΔABC: m A=90 o, m B=44 o ΔDEF: m D=90 o, m F=46 o ΔDEF: m D=90 o, m F=46 o AB C E F 9044 46 D 90 46

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Bellwork Solution Determine whether the two triangles are similar Determine whether the two triangles are similar Set 2 Set 2 ΔABC: m A=132 o, m B=24 o ΔABC: m A=132 o, m B=24 o ΔDEF: m D=90 o, m F=24 o ΔDEF: m D=90 o, m F=24 o AB C E F 13224 D 90 24

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Bellwork Solution Solve Solve

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Bellwork Solution 19xy48 She was born in the year whose sum of digits is 22 and where the units digit is She was born in the year whose sum of digits is 22 and where the units digit is twice the tens digit. What year was she born?

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Prove Triangles Similar by SSS and SAS Section 6.5

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The Concept Yesterday we looked at looked at how we can prove two triangles similar by way of looking at their angles Yesterday we looked at looked at how we can prove two triangles similar by way of looking at their angles Today we’re going to see how we can utilize some of our congruence methodologies to also prove similarity Today we’re going to see how we can utilize some of our congruence methodologies to also prove similarity

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Theorems When we studied triangle congruence we used this postulate Postulate 19: Side-Side-Side Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent… This postulate now becomes Theorem 6.2: Side-Side-Side Similarity Theorem If the corresponding side lengths of two triangles are proportional, then the triangles are similar.

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Theorem in action Let’s look at an example to illustrate this theorem Are these two triangles similar? 12 8 10 1815 12 What about these two? 12 8 10 14 12

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Theorems When we studied triangle congruence we also saw this postulate Postulate 20: Side-Angle-Side Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent This postulate now becomes Theorem 6.3: Side-Angle-Side Similarity Theorem If 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

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Theorem in action Let’s look at an example to illustrate this theorem Are these two triangles similar? 10 15 22.5

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Example Are these two triangles similar? 12 8 9 24 16 18

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Example Are these two triangles similar? 15 9 13 19

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Example Are these two triangles similar? 18 9 7 7

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Example Are these two triangles similar? A B C DE 43 21.5

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Example Which two, if any, of these triangles are similar A 12 B C J K L M N O 9 10 24 18 21 6 7 8

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Example Which two, if any, of these triangles are similar A 16 B C J K L M N O 8 1826 6 13

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Ways to use the theorem What value of x makes the two triangles similar 20 12 x+6 30 3(x-2) 21

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Example You enlarge triangle XYW to triangle JHK as shown from vanishing point P. Are the two triangles similar? P X J W K H XW=16 JK=24 YW=18 HK=27 Y 75 o

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Homework 6.5 6.5 1, 4-32 even 1, 4-32 even

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HW

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Most Important Points SSS Similarity Theorem SSS Similarity Theorem SAS Similarity Theorem SAS Similarity Theorem

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