Question Bank: Properties of Perpendicular Bisector

[nelvin898]

If angle BAD is a right angle, what is the length of side BD? AD is 5. Print screen below contains an image for better understanding.

(1) AC is perpendicular to BD

(2) BC = CD

Print screen below:



Hi,

I get kind of lost with the properties of perpendicular bisector. When I see a perpendicular bisector, I don't know what it means, except that there are two 90 degree angles formed.

Why is statement A not sufficient?

Statement A says it is a perpendicular bisector. Therefore there is a 90 degree angle, and the right angle BAD is cut 90/2 degrees, which is 45 degrees right? Forming a 45-45-90 angle, you can get length BD.

Can you explain to me why statement A is insufficient?

EDIT: Is there a diff between perpendicular vs perpendicular bisector? IS there such a thing as only bisector? :( What are the difference among the 3?

Thanks.

[mithunsam]

Statement A didn't say that AC is perpendicular bisector to BD. It just says AC is perpendicular. Hence, the statement is not sufficient.

Had it mentioned AC a perpendicular bisector, then the statement would have been sufficient. Infact, statement 1 & 2 together convey this message.

AC perpendicular to BD just means the lines are perpendicular. That means angle ACB = angle ACD = 90 degrees. However, that doesn't mean that AC divides BD into half.

Perpendicular bisector means that the lines are perpendicular and that line AC divides BD into half (BC = CD).

Angle bisector divides an angle into half.

Bisector simply means a line that divides something (angle, line etc) into half.

[nelvin898]

Statement A didn't say that AC is perpendicular bisector to BD. It just says AC is perpendicular. Hence, the statement is not sufficient.

Had it mentioned AC a perpendicular bisector, then the statement would have been sufficient. Infact, statement 1 & 2 together convey this message.

AC perpendicular to BD just means the lines are perpendicular. That means angle ACB = angle ACD = 90 degrees. However, that doesn't mean that AC divides BD into half.

Perpendicular bisector means that the lines are perpendicular and that line AC divides BD into half (BC = CD).

Angle bisector divides an angle into half.

Bisector simply means a line that divides something (angle, line etc) into half.

Another question. When you say AC is perpendicular to BD, does AC divide the 90 degree <A into half?

[mithunsam]

That will happen only when <ABD = <ADB = 45 degrees.

Consider the diagram, which you posted. Imagine that <ABD = 60, <ADB = 30 and <A = 90.

Now draw AC perpendicular to BD. We know that, <ACB = <ACD = 90.

Since <ABD = 60, <BAC has to be 30
Similarly, since <ADB = 30, <DAC has to be 60.

Here, AC divides <A to 30 & 60 degrees.

[jnelson0612]

nelvin, you have gotten some good information, but please let us know if you need further help.