Start by drawing a segment from A to any of the vertices. Use this segment to construct a 180^(∘) angle.
SE
Practice makes perfect
We are given a square with vertices E, S, Q, and R, and a point of rotation A.
We want to rotate RQ by 180^(∘) about point A. To do so, we will follow four steps.
Draw AR and construct a 180^(∘) angle with vertex A and side AR.
Construct AR' such that AR' lies on a side of the angle drawn in the previous step and AR'≅ AR.
Locate Q' in a similar manner.
Connect Q' and R' to draw R'Q'.
Let's do it!
Step 1
Let's draw AR.
We will use a protractor to construct a 180^(∘) angle with vertex A and side AR. We start by placing the center of the protractor on A, making sure that the flat part is on AR.
Notice that the inner measuring scale has 0^(∘) on AR. Therefore, we will use the inner measuring scale. Moreover, recall that unless otherwise specified, we measure the angle in the counterclockwise direction.
Finally, to construct the angle, we remove the protractor and draw a ray that starts at A and that passes through the mark we have just drawn.
Note that for this step we could have chosen point Q instead of R. We arbitrarily chose point R for simplicity.
Step 2
We will now locate R', which is the image of R 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 R.
Without modifying the angle 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 R'.
Step 3
We can repeat Steps 1 and 2 to find Q'.
Step 4
Finally, to draw R'Q' — which is the image of RQ after a rotation of 180^(∘) about A — we will connect the obtained vertices.
As we can see the image of point R is S, and image of Q is E. Therefore, the image of RQ is SE.
