IM 8.1.14 Lesson: Alternate Interior Angles

Find the measure of angle [math]JGH[/math] in the applet below. Explain or show your reasoning.[br][br]Find and label a second 30 degree angle in the diagram. Find and label an angle congruent to angle [math]JGH[/math].

Lines AC and DF are parallel. They are cut by transversal HJ.

With your partner, find the seven unknown angle measures in the diagram above. Explain your reasoning.

What do you notice about the angles with vertex [math]B[/math] and the angles with vertex [math]E[/math]?

Using what you noticed, find the measures of the four angles at point B in the second diagram. Lines AC and DF are parallel.

The next diagram resembles the first one, but the lines form slightly different angles. Work with your partner to find the six unknown angles with vertices at points B and E.

What do you notice about the angles in this diagram as compared to the earlier diagram? How are the two diagrams different? How are they the same?

Parallel lines l and m are cut by two transversals which intersect l in the same point. Two angles are marked in the figure. Find the measure x, of the third angle.

Lines l and k are parallel and t is a transversal. Point M is the midpoint of segment PQ. Find a rigid transformation showing that angles MPA and MQB are congruent.

Describe the rigid transformation you performed above.

In this picture, lines l and k are no longer parallel. M is still the midpoint of segment PQ.

Does your argument in the earlier problem apply in this situation? Explain.