In the figure above C is the midpoint of BD and AC = DE. What is the value of n ?
A. 30
B. 45
C. 60
D. Cannot be determined from the information given
Answer:B
In the figure above C is the midpoint of BD and AC = DE. What is the value of n ?
A. 30 B. 45 C. 60 D. Cannot be determined from the information given
Explanation: B Since line AE is perpendicular to the line containing segment AB and the line containing segment DE, these two lines must be parallel. Therefore, ∠ABC is equal to ∠CDE because they are both small angles created by a line crossing two parallel lines. Since ∠DCE and ∠ACB are opposite each other, they must be equal as well, so these are two similar right triangles. The question also tells you that C is the midpoint of BD, which means that BC and CD are equal. When you have two sides and the included angle of one triangle congruent to two sides and the included angle of a second triangle, you know that the triangles are congruent. This means that AB = DE and AC = CE. Lastly, the question states that AC = DE, which means that AB = AC, and these must be isosceles right triangles. Angle ABC is therefore 45°, and n, which is opposite ∠ABC, must be 45° as well. The correct answer is (B).