Question

1. given the rotation of △abc shown below, determine the counter - clockwise angle of rotation that occurred about point d. show all relevant lines and measurements you made to determine your answer.
2. using only a straightedge and a compass, construct the image of △efg after a rotation by 180° about point k shown. leave all construction marks. mark the image △efg.
3. construct a line (overline{ab}) such that it is parallel to (overline{rs}) shown below. use only a straightedge and compass. leave all construction marks. (hint: plot a third point not on the line and rotate about this point.)

Explanation:

Step1: Identify key - point for angle measurement

Connect point D to corresponding vertices (e.g., A and A'). Measure the angle between DA and DA' using a protractor.

Step2: Determine the counter - clockwise angle

Read the angle value in the counter - clockwise direction from DA to DA'.

For question 2:

Step1: Connect vertices to point K

Connect E, F, G to point K with a straightedge.

Step2: Extend lines

Extend the lines EK, FK, GK.

Step3: Measure equal distances

Using a compass, measure the distance from E to K, then mark the same distance on the extended EK on the opposite side of K to get E'. Do the same for F and G to get F' and G'.

Step4: Connect new vertices

Connect E', F', G' to form △E'F'G'.

For question 3:

Step1: Plot a point

Plot a point P not on line RS.

Step2: Draw arcs

With the compass, draw an arc from a point on RS (say R) that intersects RS at one point and then draw the same - radius arc from point P.

Step3: Measure arc length

Measure the arc length on RS between the intersection points of the arc and RS.

Step4: Transfer arc length

Transfer the arc length from RS to the arc drawn from P.

Step5: Draw parallel line

Draw a line through P and the new intersection point on the arc from P to get line AB parallel to RS.

Answer:

For question 1: The counter - clockwise angle value obtained from measurement.
For question 2: △E'F'G' constructed as described.
For question 3: Line AB constructed parallel to RS.