Alternate Interior Angles

Lines AB and FC are parallel. Line BC is a transversal. Use points A, B, and C to move the lines. Observe the angle values.

<ABC and <HCB are alternate interior anlges.

———————————————————————————————————————————————————

To Investigate Angle Properties Between Intersecting Lines.

(A). The applet below shows two lines that intersect at G.

(1). Find the measure of angle  JGH in the applet above.  Explain or show your reasoning.

(2). Find and label a second 30 degree angle in the diagram. Find and label an angle congruent to angle JGH.

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

(1). Find the seven unknown angle measures in the diagram above. Explain your reasoning.

(2). What do you notice about the angles with vertex  B  and the angles with vertex  E ?

(C). The diagram below resembles the previuos 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.

(1). What do you notice about the angles in this diagram as compared to the earlier diagram?

(2). How are the two diagrams different? How are they the same?

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

———————————————————————————————————————————————————

More Investigation of Angle Properties Between Intersecting Lines.

(A). Parallel lines l and m are cut by two transversals that intersect l in the same point. Two angles are marked in the figure.

Find the measure x, of the third angle.

(B). 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.

(C). The diagram shows three lines with some marked angle measures.

Find the missing angle measures marked with question marks.

(D). Lines s and t are parallel.

Find the value of x.

———————————————————————————————————————————————————

Find Angles Between Intersecting Lines.

Use the diagram to find the measure of each angle.

(1). m∠ABC = ?

(2). m∠EBD = ?

(3). m∠ABE = ?

———————————————————————————————————————————————————

Lines s and t are parallel. Find the value of x.

———————————————————————————————————————————————————

Lines k and l are parallel, and the measure of angle ABC is 19 degrees.

(1). Explain why the measure of angle  BCF  is 19 degrees. If you get stuck, consider using the applet to translate line   by moving B to C.

(2). What is the m∠BCD? Explain.

———————————————————————————————————————————————————

The two figures are scaled copies of each other.

(1). What is the scale factor that takes Figure 1 to Figure 2?

(2). What is the scale factor that takes Figure 2 to Figure 1?