LFP+Mathematical+Reflections,+p+40+0910

SM 10/25/09 Math 8 F MATHEMATICAL REFLECTIONS 3 

BIG Idea: The dimensions of a right triangle can be determined with limited information. Essential Questions: How can I find the perimeter of a right triangle? Notes- To determine if a triangle is a right triangle only by knowing the sides, you must add the two legs together in the form of  a² + b² = c², (leg 1 is a and a is leg 2) the answer must be c², if not, then the triangle is not a right triangle, but if yes, it is. For example, the two legs could be 3 and 2, the hypotenuse is // √13 //, a² + b² = c², 3 is a and 2 is b, c is the hypotenuse, 3² + 2² = // √ //13², 9 + 4 = 13, 13 = 13, so this triangle is a right triangle. You can find out the hypotenuse by using the Pythagorean Theorem,  a² + b² = c², a and b are the legs, and c is the hypotenuse. Instead of doing the Pythagorean Formula, you write  a² - c² = b². (a is leg 1, b is leg 2, and c is the hypotenuse) You draw a line to connect the dots, and make the line into a side of square. Then make an outer square which will be somehow touching the inner squares four corners. Then count how many boxes are inside the outer square in total. (You make the boxes by joining the dots and making them into a grid) Finally count the extra boxes outside the inner square but inside the outer square. (Some of the boxes may be cut off. You must join all the cut ones together. For example if there are two half boxes, it makes 1 whole box.) Then subtract the extra boxes from the total number of boxes. The answer will be the area of the inner square. To find the side (which is the original line), square root the area of the inner square. Sometimes the area will be in decimal approximation, then we leave the length with the square root symbol. (Answer same as notes) You must add the two legs together in the form of  a² + b² = c², (a is leg 1 and  b is leg 2) the answer must be  c², if not, then the triangle is not a right triangle, but if yes, it is. For example, the two legs could be 3 and 2, the hypotenuse is // √ //13, a² + b² = c², 3 is a and 2 is b, c is the hypotenuse, 3² + 2² = // √ //13²  , 9  + 4 = 13, 13 = 13, so this triangle is a right triangle. ** Summary: ** In this unit, we learnt how to use the Pythagorean Theorem and how to use it to find lengths, areas, types of triangles, and perimeters.
 * 1.)  **** a. Suppose you are given the lengths of the legs of a triangle. Describe how you can find the length of the hypotenuse **
 * b. Suppose you are given the lengths of one leg and the hypotenuse of a right triangle. Describe how you can find the length of the other leg. **
 * 2.)  ** ** Describe how you can use the Pythagorean Theorem to find the distance between two dots on a sheet of dot paper without measuring. **
 * 3.)  ** ** How can you determine whether a triangle is a right triangle if you know only the lengths of its three sides? **