Question

Use the figure to complete each statement.

Answer 1

a. ∠BEC = 90°, so CD is the perpendicular of AB
b. AE = EB ⇒ EB = AB/2, so EB = 5
c. AE = EB ⇒ AE =
`(1)/(2)` AB
d. AE = EB ⇒ E is the midpoint of AB
e. CD is the perpendicular of AB, so ∠BED = 90°

Answer 2

Explanation:

From the figure, it is given that AE=EB and m∠E=90°.

Now,

1. From the figure, it can be seen that the angle E is forming a right angle on the line AB, thus CD is the perpendicular of AB.

2. From the figure, we can see that AE=EB, therefore if AB=10, then
`EB=(1)/(2)AB`, therefore
`EB=(1)/(2)(10)`⇒
`EB=5`.

3. Also, it can be seen that
`AE=(1)/(2)AB`.

4. Now, AE is equal to EB, which implies that E is the midpoint of AB.

5. Also, CD is the perpendicular of AB, therefore ∠BED = 90°.