Question

To win a local billiards tournament, all Jeanette has left to do is drop the 9-ball. Because of the other balls on the table (not shown), her only realistic shot on this turn is to bounce the ball off both sides of the table as shown. Use the information in the image to answer the questions below. Lines AB and CH are parallel, and the near side of the table is parallel to the far side.

a. What other angle measures can we be sure about? Explain your reasoning.
b. Identify the sets of congruent angles. Explain your conclusions.
c. Identify all the sets of alternate interior angles you can envision. Explain.
d. Identify all the sets of corresponding angles. Explain.

Answer 1

Here's what I get.

Explanation:

Assume the diagram is like the one below.

Segments AB, BC, and CH are transversals to the sides of the pool table.

BC is also a transversal to AB and CH.

a. Angles we can be sure about

∠ABC — interior opposite angles of transversal BC

∠CBH — interior opposite angles of transversal BC

∠BHC — interior angles of triangle BHC

∠ABK — alternate exterior angles of transversal BC

∠CHG — complementary to ∠CGH

b. Sets of congruent angles

∠ABC ≅ ∠BCH = 66° — interior opposite angles of transversal BC

∠CBH ≅ ∠BCE = 57° — interior opposite angles of transversal BC

∠BHC ≅ ∠GCH = 57° — interior opposite angles of transversal CH

∠ABK ≅ ∠GCH = 57° — alternate exterior angles of transversal BC

One set of congruent angles is {∠ABC, ∠BCH}

Another set is {∠ABK, ∠BCE, ∠BHC, ∠CBH, ∠GCH}

c. Alternate interior angles

Alternate interior angles are a pair of angles on the inner sides of the parallel lines but on opposite sides of the transversal.

The sets of alternate interior angles are {∠ABC, ∠BCH}, {∠ ABC, ∠BCD} {∠BCE, ∠CBH}, {∠CHJ, ∠GCH}

d. Corresponding angles

Corresponding angles are a pair of angles on the same side of parallel lines and on the same side of the transversal.

The diagram has no corresponding angles.