TODAY IN GEOMETRY… Independent Practice Learning Target 1: Review Ch. 5 concepts-Triangle Midsegments, Centroids and Inequalities Mini Quiz-TODAY! Learning Target 2: Simplifying Radicals Independent Practice

MIDSEGMENT THEOREM: The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. 𝐵 𝐷𝐸 ∥ 𝐴𝐶 𝐷𝐸= 1 2 𝐴𝐶 𝐸 𝐷 𝐴 𝐶

If the perimeter of △𝑅𝑆𝑇=68 𝑖𝑛𝑐ℎ𝑒𝑠, find the perimeter of △𝑈𝑉𝑊. △𝑈𝑉𝑊= 1 2 (68) If 𝑉𝑊=2𝑥−4 and 𝑅𝑆=3𝑥−3, what is 𝑉𝑊? 2 𝑉𝑊 =𝑅𝑆 2 2𝑥−4 =3𝑥−3 4𝑥−8=3𝑥−3 − 3𝑥 − 3𝑥 𝑥−8=−3 + 8 + 8 𝒙=𝟓 𝑉𝑊=2𝑥−4 𝑉𝑊=2 5 −4=6 𝑆 𝑈 𝑉 𝑅 𝑊 𝑇 1. If 𝑈𝑉=13, find 𝑅𝑇. 𝑅𝑇=2 𝑈𝑉 =2 13 =26 2. If 𝑆𝑇=20, find 𝑈𝑊. 𝑈𝑊= 1 2 𝑆𝑇 = 1 2 20 =10

A different way to think about this: CONCURRENCY OF MEDIANS: The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. 𝐴𝑃= 2 3 𝐴𝐵 𝐴 A different way to think about this: 𝐴𝑃 is twice as long as 𝐵𝑃 OR 𝐵𝑃 is half of 𝐴𝑃 𝟐𝒙 𝑃 𝒙 𝐵 CENTRIOD

PRACTICE: 𝑃 is the centroid of △𝐴𝐷𝐸, 𝐶𝐸=27 𝐵 𝐶 𝐸 𝐹 1. 𝐹𝐸= 2. 𝐶𝑃= 3. 𝑃𝐸= 4. 𝐹𝑃= 5. 𝐹𝐷= 6. 𝐴𝐸= 𝐴𝐹=12 12 1 3 𝐶𝐸=9 2 3 𝐶𝐸=18 1 2 𝐷𝑃=3 6 𝐹𝑃+𝑃𝐷=9 2𝐴𝐹=24

𝐴𝐵+𝐵𝐶>𝐴𝐶 𝐵𝐶+𝐴𝐶>𝐴𝐵 𝐴𝐶+𝐴𝐵>𝐵𝐶 TRIANGLE INEQUALITY THEOREM: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. 𝐶 𝐵 𝐴 𝐴𝐵+𝐵𝐶>𝐴𝐶 𝐵𝐶+𝐴𝐶>𝐴𝐵 𝐴𝐶+𝐴𝐵>𝐵𝐶

𝐴𝐵 < 𝐵𝐶 < 𝐴𝐶 Triangle inequalities: ∠𝐶=35° ∠𝐴=45° ∠𝐵=110° 𝑎 𝑐 𝐶 𝑏 𝐴 𝐴𝐵 < 𝐵𝐶 < 𝐴𝐶 The longest side of a triangle is opposite the largest angle. The smallest side of a triangle is opposite the smallest angle. 𝒔𝒊𝒅𝒆 𝒃 𝒊𝒔 𝒕𝒉𝒆 𝒍𝒐𝒏𝒈𝒆𝒔𝒕 𝒔𝒊𝒅𝒆 𝒔𝒊𝒅𝒆 𝒄 𝒊𝒔 𝒕𝒉𝒆 𝒔𝒉𝒐𝒓𝒕𝒆𝒔𝒕 𝒔𝒊𝒅𝒆

YES, IT IS POSSIBLE TO CONSTRUCT THIS TRIANGLE! PRACTICE: Is it possible to construct a triangle with the sides 3, 7, 9? 1. Smallest possible value can be found by subtracting the two largest numbers. 2. Greatest possible value can be found by adding the two smallest numbers. smallest value:𝑥>9−7 𝒙>𝟐 largest value:𝑥<3+7 𝒙<𝟏𝟎 Check smallest given side….3 𝟑>𝟐 Check greatest given side….9 𝟗<𝟏𝟎 YES, IT IS POSSIBLE TO CONSTRUCT THIS TRIANGLE!

CHAPTER 5 QUIZ You have 10 minutes to complete your test Are you prepared? Pencil? Calculator? Ch.5 Yellow notes allowed If you finish early: Finish any missing assignments. Work on something quietly as the rest of your fellow classmates complete their test. NO TALKING. STAY IN YOUR SEATS. RETURN ANY BORROWED BOOKS AND CALCULATORS. Turn in any missing or corrected assignments.

Perfect Squares: 1 4 9 16 25 36 49 64 81 100 121 144 SIMPLIFYING RADICALS: 1. 81 2. 25 3. 72 4. 48 5. 175 6. 300 =9 =5 𝑃𝑒𝑟𝑓𝑒𝑐𝑡 𝑆𝑞𝑢𝑎𝑟𝑒 𝑃𝑒𝑟𝑓𝑒𝑐𝑡 𝑆𝑞𝑢𝑎𝑟𝑒 = 36·2 = 36 · 2 =6 2 = 16·3 = 16 · 3 =4 3 = 25·7 = 25 · 7 =5 7 = 100·3 = 100 · 3 =10 3

Perfect Squares: 1 4 9 16 25 36 49 64 81 100 121 144 SIMPLIFYING RADICALS WITH VALUES IN FRONT: 1. 4 81 2. −8 25 3. 2 72 4. −9 48 =4·9 =−8·5 =36 =−40 =−9 16·3 =−9( 16 · 3 ) =−9 4 3 = −9·4 3 =−36 3 =2 36·2 =2( 36 · 2 ) =2 6 2 =(2·6) 2 =12 2

Perfect Squares: 1 4 9 16 25 36 49 64 81 100 121 144 MULTIPLYING AND SIMPLIFYING RADICALS: 1. 5 · 10 2. − 4 · 25 3. 2 72 ·2 3 4. −2 48 ·3 2 = 5·10 =− 4·25 = 50 = 25·2 = 25 · 2 =𝟓 𝟐 =− 100 =−𝟏𝟎 =(2·2)( 72·3 ) =4 216 =4 6·36 =4 6 · 36 =(4·6) 6 =𝟐𝟒 𝟔 = −2·3 48·2 =−6( 96 ) =−6( 16·6 ) =−6( 16 · 6 ) = −6·4 6 =−𝟐𝟒 𝟔

Simplified Radical Form (SRF) HOMEWORK #1: Simplified Radical Form (SRF) Half sheet