Pythagoras Lessons

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Information Report
Category:

Documents

Published:

Views: 3 | Pages: 5

Share
Related documents
Description
1 Vocabulary: 3 5 0.75 which can bewritten as aratio is called arational number and 2 which can't bewritten as ratios arecalled irrational numbers or or thesymbol is called aRADICAL n thenumber beneath the t radical sign is theRADICAND n is theprincipal or positivesquareroot of n n is thenegativesquareroot of n n isthepositiveor negativesquareroot of n ÷ ± n is thepositiveor negativesquareroot of n ± What is the approximate value of these radicals? Think about how close they are to the
Tags

Elementary Mathematics

Transcript
2 Solving Equations with Radicals 2 there are actually two solutions. Can you think of them both? x4  which is written as 2 x2 or 2    The rest of the steps in solving equations just use the reverse operations that we have used before. 2 2x39   2 add 3 on both 2x12 sides  2 divide 2 on both s6sx ide  square root on both sx6 ides   2 3x152   2 add 1 on both 3x6 2sides  2 multiply by 2 on both 3x12sside  divide by 3 on both s4sx ide  square root on both sdsxie 2   2 3x154  2 multiply by 4 on bot3x12h 0essid    2 add 1 on both 3x21 sides  2 divide by 3 on both s7sx ide  suare root on both sx7 ides  2 2x45117   2 minus 5 on bot2xh 46s7side  2  72x o44n.s2 b    2  4 o2x3.s8n b   2  2 onsx19 b.   x19   2 4.2x165  x7  2 3x2452.    x10  2 3(m1)63.2  m3   2 1.5y411   y2  2 4g21035.    g3   2 5(h1)16.9    h3   2 y.273 3   y2   22 5n11382n.     n2  2 3z289.5   z10  2 53b110.2     bno solution  2 3(5z1411.2)7   z2  2 52(4t11121.)    t1   Finding the Area of Complex Shapes–see Looking For Pythagoras. Investigation 2 1. Make a rectanglearound the shape.2. Make triangles and rectangles in the outside.  A  BCDE n e area o e recane.     Find the area of the outside shapes.12B12   11A0.52   C212    22D22   31E1.52   Find the total outside area7  Subtract the area of the outside fromthe rectangle area to get the inside area.5  Find the area of the rectangle.5420    BC ADE Find the area of the outside shapes.B212    32A32   12C12   41E22   Find the total outside area14  Subtract the area of the outside fromthe rectangle area to get the inside area.6  34D62    3 Finding the Length of Segments–see Looking For Pythagoras. Page20 Make a squarearound the segment.Counting the number of dots on each side makes it easy. n e area o e ouse square.     Find the area of the outside triangles. ) 514(102   Find the area of the inside square.361026    Therefore the length of one sideof the square is26n e area o e ouse square.     Find the area of the outside triangles. ) 324(122   Find the area of the inside square.251213    Therefore the length of one sideof the square is13 Pythagorean Theorem. See page 482 in the textbook.In a right triangle the area of a square on the hypotenuse is equal to the sum of the area of the squares on the other two sides. Note: The hypotenuse is the long side of the triangle. It is opposite the right angle. 222 abc   The sum of the areas gives the equation: When the hypotenuse is the unknown. 222 abc   222 35x   34x  x34  When a leg is the unknown. 222 abc   222 5x11   222 x115   2 x96  x96  x46   4 When the side lengths include variables. 222 abc   222 (2x)(3x)8   22 4x9x64   2x83x 2 13x64  64x13  813  222 abc       222 5p67p   222 25p649p   22 624p  2  p2  3 p2  When there is more than one triangle in the diagram. 222 98y   Choose the triangle where you know two sides. Label the third side with a variable. 2 145y  Note: We don’t need to know what y is. Solve the other triangle. 222 yx13   2 22 we know y145 so 145x13     22 x13145   2 x24  x24  x26  Dot Paper Problems:Find the perimeter of this shape.Construct right triangles and then solve using Pythagoras. 22 x    22 y5229     perimeter4132925     22 z422025     Find the perimeter for these shapes. 21062512    812520    333532    3105245    21321035282     621310   5132765751     Questions Involving Recognising Pythagorean Relationships:1. Recognising right triangles:Are the following triangles right triangles?The sides of a right triangle will make the Pythagoras equation true. Try it for this triangle 697 222 679   364981   8581   Not true so not a right triangle. 152016729054 222 151620   481400   Not true so nota right triangle. 222 121620   400400  True so it isa right triangle. 162012 222 547290   81008100  True so it isa right triangle.
Recommended

14 pages

44 pages

19 pages

18 pages

17 pages

14 pages

11 pages

92 pages

68 pages

12 pages

6 pages

50 pages

40 pages

7 pages

18 pages

View more...