In the illustration, $\overline { A B } \| \overline { C D }$ . Is triangle ABO similar to triangle CDO? Why or why not?
A) No, OC is three times as long as BO is.
B) Yes, all angles of ABO are equal to corresponding angles of DCO.
C) Neither of the other explanations is correct.

Question

In the illustration, $\overline { A B } \| \overline { C D }$ . Is triangle ABO similar to triangle CDO? Why or why not? 
A) No, OC is three times as long as BO is. 
B) Yes, all angles of ABO are equal to corresponding angles of DCO. 
C) Neither of the other explanations is correct.

Quizplus · Accepted Answer

Since AB and CD are parallel, we know that ∠A = ∠D and ∠B = ∠C (corresponding angles are equal). Additionally, we know that ∠OAB and ∠OCD are both right angles (given in the illustration). Therefore, triangle ABO and triangle CDO both have a right angle and two equal angles, making them similar by the Angle-Angle (AA) similarity theorem.

In the Illustration AB‾∥CD‾\overline { A B } \| \overline { C D }AB∥CD

In the Illustration $\overline { A B } \| \overline { C D }$