Rigid Transformations, Angles and Congruence

Draw

Draw parallel lines $$AB$$ and $$CD$$ .

Draw

Pick any point $$E$$ . Rotate $$AB$$ $$90^\circ$$ clockwise around $$E$$ .

Draw

Rotate line $$CD$$ $$90^\circ$$ clockwise around $$E$$ .

Multiple Choice

What do you notice after rotating lines $$AB$$ and $$CD$$ $$90^\circ$$ clockwise around point $$E$$ ?

• Lines AB and CD will remain parallel after the rotation.
• Lines AB and CD will overlap completely after the rotation.
• Lines AB and CD will rotate to form a straight line.
• Lines AB and CD will be perpendicular to their original positions after the rotation.

Open Ended

Find the measure of angle ABC using the diagram. Explain your reasoning.

Open Ended

Find the measure of angle $$EBD$$ using the diagram. Explain your reasoning.

Open Ended

Find the measure of angle $$ABE$$ using the diagram. Explain your reasoning.

Multiple Choice

Where is the point $$R$$ located so that a $$180^\circ$$ rotation with center $$R$$ sends $$P$$ to $$Q$$ and $$Q$$ to $$P$$ ?

• The point P itself.
• The point Q itself.
• A point outside the line segment PQ.
• The midpoint of P and Q.

Multiple Choice

Is there more than one point $$R$$ that works for part a?

• There are infinitely many points R that work for part a.
• Yes, there is more than one point R that works for part a.

Open Ended

Which of the lines in the picture is parallel to line $$\ell$$ ? Explain how you know. Three lines, m, k and l, cut by a transversal, p. Lines k and l will not intersect no matter how far they extend. Line m appears to be angled towards lines k and l on the right so that it would intersect them at a point not shown.