chapter 5 sol problems
DESCRIPTION
Modified and Animated By Chris Headlee Nov 2011. SOL Problems; not Dynamic Variable Problems. Chapter 5 sol problems. SSM: Super Second-grader Methods. Triangles and Logic. SSM: measure sides with scrap paper AC is shortest BC is longest. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/1.jpg)
SSM: Super Second-grader Methods
Modified and Animated By Chris HeadleeNov 2011
CHAPTER 5 SOL PROBLEMS
SOL Problems; not Dynamic Variable Problems
![Page 2: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/2.jpg)
Triangles and Logic
Order the measures of angles from largest to smallest: 75 > 55 > 50Replace with the letter of the angles A > C > BPut in the missing letters of the triangle BC > AB > ACNow the sides are ordered from longest to shortest: BC > AB > BD
SSM:•measure sides with scrap paper•AC is shortest•BC is longest
![Page 3: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/3.jpg)
Triangles and Logic
Order the measures of sides from smallest to largest: 150 < 245 < 365Replace with the letters of the sides HI < HJ < IJPut in the missing letters of the triangle J < I < HNow the angles are ordered from smallest to largest: J < I < H
SSM:•largest angle opposite largest side
![Page 4: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/4.jpg)
Triangles and Logic
third side must:14 – 8 < 3rd side < 14 + 8 6 < 3rd side < 22
all answers except A fit inequality above
SSM:•any two sides bigger than 3rd
![Page 5: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/5.jpg)
Triangles and Logic
Order the measures of sides from largest to smallest: 11 > 8 > 7Replace with the letter of the sides GR > BR > BGPut in the missing letter of the triangle B > G > RNow the angles are ordered from largest to smallest: B > G > R
SSM:•Remember the virtual alligatorlargest stick largest mouth
![Page 6: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/6.jpg)
Triangles and Logic
Take the smallest two numbersadd them togetherif they are greater than the third, then we can have a triangle
SSM:•try and graph it on graph paper
![Page 7: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/7.jpg)
Triangles and Logic
Order the measures of angles from smallest to largest: 40 < 60 < 80Replace with the letter of the angles D < B < CPut in the missing letters of the triangle BC < CD < BDNow the sides are ordered from smallest to largest: BC < CD < BD
SSM:•Measure the sides with ruler or scrap paper•BC is the shortest•BD the longest
![Page 8: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/8.jpg)
Triangles and Logic
Take the smallest two numbersadd them togetherif they are greater than the third, then we can have a triangle
SSM:•same procedures as normal
![Page 9: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/9.jpg)
Triangles and Logic
Order the measures of sides from smallest to largest: 12 < 15 < 19Replace with the letter of the sides QR < PQ < PRPut in the missing letter of the triangle P < R < QNow the angles are ordered from largest to smallest: P < R < Q
SSM:•Remember the virtual alligatorlargest stick largest mouth
![Page 10: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/10.jpg)
Triangles and Logic
Angles: A = 60, C = 50 and B must be 70 (3 angles = 180)
Since BC is opposite the 60° angle it is the middle length side, and must be between 10 (smallest) and 12 (longest)
SSM:•Use ruler or scrap paper to measure AB and estimate BC
![Page 11: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/11.jpg)
Triangles and Logic
two smallest sides added together > biggest side
A fails because its two smallest sides = biggest side
SSM:•not 3 triangles and one not
![Page 12: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/12.jpg)
Triangles and Logic
Arrange sides from smallest to largest based on numbers 6, 8, 10Substitute the side’s names (line segments) EF, DE, DFPut in missing letter from triangle D, F, EAngles are now from smallest to largest
SSM:•virtual alligator•Largest stick largest angle•DF is biggest so E is biggest•EF is smallest so D is smallest
![Page 13: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/13.jpg)
Triangles and Logic
Arrange angles from smallest to largest based on given C, B, APut in missing letters from triangle AB, AC, BCSides are now from smallest to largest
SSM:•virtual alligator•Largest angle largest stick•A is biggest so BC is biggest•C is smallest so AB is smallest
![Page 14: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/14.jpg)
Triangles and Logic
Order the measures of angles from smallest to largest: 45 < 65 < 70Replace with the letter of the angles K < J < LPut in the missing letters of the triangle LJ < LK < JKNow the sides are ordered from smallest to largest: LJ < LK < JK
SSM:•Measure the sides with ruler or scrap paper•LJ is the shortest•JK the longest
![Page 15: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/15.jpg)
Triangles and Logic
smallest side, 50, is opposite the smallest angle, X or ZXY
SSM:•virtual alligator•smallest angle is opposite the smallest angle
![Page 16: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/16.jpg)
Triangles and Logic
Take the smallest two numbersadd them togetherif they are greater than the third, then we can have a triangle
Three will work and one will not
SSM:•try and graph it on graph paper
![Page 17: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/17.jpg)
Triangles and Logic
Take the smallest two numbersadd them togetherif they are greater than the third, then we can have a triangle
J does not work
SSM:•three work•one does not
![Page 18: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/18.jpg)
Triangles and Logic
Order the measures of sides from smallest to largest: 15 < 16 < 17Replace with the letter of the sides XY < YZ < XZPut in the missing letter of the triangle Z < X < YNow the angles are ordered from smallest to largest: Z < X < Y
SSM:•Remember the virtual alligatorsmallest stick smallest mouth
![Page 19: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/19.jpg)
Triangles and Logic
Order the measures of angles from smallest to largest: 15 < 65 < 100Replace with the letter of the anglesB < A < CPut in the missing letters of the triangle AC < BC < ABNow the sides are ordered from smallest to largest: AC < BC < AB
SSM:•Remember the virtual alligatorsmallest stick smallest mouth
![Page 20: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/20.jpg)
Triangles and Logic
Arrange sides from smallest to largest based on numbers 56, 64, 70Substitute the side’s names (line segments) PQ, PR, QRPut in missing letter from triangle R, Q, PAngles are now from smallest to largest
SSM:•virtual alligator•Largest stick largest angle•QR is biggest so P is biggest•PQ is smallest so R is smallest
![Page 21: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/21.jpg)
Triangles and Logic
two smallest sides added together > biggest side
C fails because its two smallest sides = biggest side
SSM:•not 3 triangles and one not
![Page 22: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/22.jpg)
Triangles and Logic
two smallest sides added together > biggest sideif AC is biggest then AC < 1208 (650+558)if AC is smallest then AC > 92 (650-558)
SSM:•by looks AC is biggest side so its got to be bigger than 650•this eliminates F and G
![Page 23: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/23.jpg)
Triangles and Logic
Order the measures of sides from smallest to largest: 5 < 6 < 7Replace with the letter of the sides BC < AC < ABPut in the missing letter of the triangle A < B < CNow the angles are ordered from largest to smallest: A < B < C
SSM:•Remember the virtual alligatorlargest stick largest mouth
![Page 24: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/24.jpg)
Triangles and Logic
Any two sides of a triangle must be bigger than the third
SSM:•not much help
![Page 25: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/25.jpg)
Triangles and Logic
Order the measures of angles from smallest to largest: 50 < 60 < 70Replace with the letter of the angles C < B < APut in the missing letters of the triangle AB < AC < BCNow the sides are ordered from largest to smallest: AB < AC < BC
SSM:•Remember the virtual alligatorlargest stick largest mouth
![Page 26: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/26.jpg)
Triangles and Logic
Order the measures of angles from smallest to largest: 57 < 59 < 64Replace with the letter of the angles C < B < APut in the missing letters of the triangle AB < AC < BCNow the sides are ordered from largest to smallest: AB < AC < BC
SSM:•Remember the virtual alligatorlargest stick largest mouth
![Page 27: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/27.jpg)
Triangles and Logic
Order the measures of angles from smallest to largest: 20 < 35 < 125Replace with the letter of the angles A < B < CPut in the missing letters of the triangle BC < AC < ABNow the sides are ordered from largest to smallest: BC < AC < AB
SSM:•Remember the virtual alligatorsmallest stick smallest mouth
![Page 28: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/28.jpg)
Triangles and Logic
To make a triangle any two sides has to be greater than the third side
the distance between Chadwick and Barkersville has to be between:
90 – 70 = 20 and 90 + 70 = 160
only answer C is 20 < distance < 160
SSM:•Use ruler or scrap paper to measure AB and estimate BC
![Page 29: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/29.jpg)
Triangles and Logic
Order the measures of angles from smallest to largest: 45 < 65 < 70Replace with the letter of the angles A < B < CPut in the missing letters of the triangle BC < AC < ABNow the sides are ordered from largest to smallest: BC < AC < AB
SSM:•Remember the virtual alligatorlargest stick largest mouth
![Page 30: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/30.jpg)
Triangles and Logic
Take the smallest two numbersadd them togetherif they are greater than the third, then we can have a triangle
answers F, G and H all fail the test
SSM:•three can’t and only one works
![Page 31: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/31.jpg)
Triangles and Logic
Order the sides from smallest to largest: 4,123 < 4,472 < 5,385Replace with the letter of the sides AC < AB < BCPut in the missing letter of the triangle B < C < Aangles from largest to smallest: B < C < A
SSM:•Remember the virtual alligatorlargest stick largest mouth
![Page 32: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/32.jpg)
Triangles and Logic
Arrange angles from greatest to least 72, 60, 48Substitute the angle’s names C, B, APut in missing letters from triangle AB, AC, BCSides are now from greatest to least
SSM:•virtual alligator•Largest stick largest angle• C is biggest so AB is biggest•A is smallest so BC is smallest
![Page 33: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/33.jpg)
Triangles and Logic
Missing angle: 180 – (58+68) = 54Arrange angles from greatest to least 68, 58, 54Substitute the angle’s names B, A, CPut in missing letters from triangle AC, BC, ABSides are now from greatest to least
SSM:•not to scale!!!•virtual alligator•Largest stick largest angle• C is smallest so AB is smallest•B is biggest so AC is largest
![Page 34: Chapter 5 sol problems](https://reader033.vdocuments.site/reader033/viewer/2022061509/5681377c550346895d9f1515/html5/thumbnails/34.jpg)
Triangles and Logic
Arrange sides from smallest to largest AB, BC, ACPut in missing letter from triangle C, A, BAngles are now from smallest to largest
SSM:•virtual alligator•Largest stick largest angle•B is biggest (its obtuse!)