Construct triangle XYZ in which|YZ|=4cm, angle YZY=135°and |XZ|=8cm. measure|XY|.
Yes I want you to show me how to construct a triangle
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To construct triangle XYZ, follow these steps:
Step 1: Draw a line segment YZ of length 4 cm. This will be one side of the triangle.
Step 2: At point Y, construct an angle with a measure of 135°. To do this, use a protractor and draw a ray extending from Y. Measure an angle of 135° starting from the initial side of the ray.
Step 3: From the vertex of the angle, mark a point X on the opposite side of the angle.
Step 4: Draw a line segment XZ of length 8 cm, connecting X and Z.
Step 5: The triangle XYZ is now constructed.
To measure the length of XY, you can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In triangle XYZ, we need to determine if it is a right-angled triangle. If angle YZY is 90°, then XYZ would be a right-angled triangle. However, since angle YZY is given as 135°, the triangle is not a right-angled triangle.
Therefore, we cannot directly apply the Pythagorean theorem in this case. We need more information to determine the length of XY.
I would use graph paper.
notice 135° = 90+45 ° , so a 45° is easy to draw on a grid, simply use the diagonal
of a large square on your grid.
then measure 4 cm and 8 cm on the arms of the angle and join their end points.
Measure the missing side