Mid-Chapter Quiz
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We are given a quadrilateral with vertices A, B, C, and D, and a point of rotation A.
We want to rotate the quadrilateral ABCD by 40^(∘) about point A. To do so, we will follow four steps.
Let's do it!
We will use a protractor to construct a 40^(∘) angle with vertex A and side AC. We start by placing the center of the protractor on A, making sure that the flat part is on AC.
Notice that the inner measuring scale has 40^(∘) on AC. Therefore, we will use the inner measuring scale. Moreover, recall that if it is not specified we measure the angle in the counterclockwise direction.
Finally, to construct the angle, we remove the protractor and draw a ray from A that passes through the mark we have just drawn.
Note that for this step we could have chosen point B or point D instead of C. We arbitrarily chose point C for simplicity.
We will now locate C', which is the image of C after the rotation. To do so we will use a compass. We will start by placing the sharp spike of the compass at A, and the leg with the pencil at C.
Without modifying the amplitude of the compass, we will keep the sharp spike at A. Then we will draw an arc intersecting the ray we drew in the previous step. This point of intersection is C'.
We can repeat Step 1 and 2 to find B'.
Then we can repeat the same steps to locate D'.
