Unit 2- Triangles and Quadrilaterals in the coordinate plane Unit 2- content adapted from Deerfield Academy and Penner 1 1.Let A = (2, 4), B = (4, 5), C = (6, 1), T = (7, 3), U = (9, 4), and V = (11, 0). Triangles TUV are specially related to each other in some way. Make calculations to discover and justify the relationship that you claim. Write a few words to describe what you discover.2.A triangle that has at least two sides of equal length is called isosceles. Make up an example of the coordinates of an isosceles triangle, one of whose vertices is (3, 5). Give the coordinates of the other two vertices. Try to find a triangle that does not have any horizontal or vertical sides. 3.Show that the triangle formed by the lines y = 2x − 7, x + 2y = 16, and 3x + y = 13 is isosceles. Show also that the lengths of the sides of this triangle fit the Pythagorean equation. Can you identify the right angle just by looking at the equations? 4.The perimeter of an isosceles right triangle is 24 cm. What are the lengths of the sides of the triangle? 5.A triangular plot of land has boundary lines of 45 meters, 60 meters, and 70 meters. The 60 meter boundary runs north-south. Is there a boundary line for the property that runs due east-west? 6.In baseball, the bases are placed at the corners of a square whose sides are 90 feet long. Home plate and second base are at opposite corners. How far is it from home plate to second base to two decimal places? 7.A right triangle has one leg twice as long as the other and the perimeter is 18. Find the three sides of the triangle. 8.One of the legs of a right triangle is twice as long as the other and the perimeter of the triangle is 28. Find the lengths of all three sides, to three decimal places. 9.Two of the sides of a right triangle have lengths and . Find the possible lengths for the third side. 10.A right triangle has a 24-cm hypotenuse which is twice as long as its shorter leg. In simplest radical form, find the lengths of all three sides of this triangle. 11.The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments, whose lengths are 8 inches and 18 inches. How long is the altitude? 12.Given the points K = (-2, 1) and M = (3,
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