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# How to prove angles are complementary?

Given segment CD is perpendicular to segment AB, and segment CD bisects segment AB how do I prove that angle ACD and angle CBD are complementary angles.

The picture looks something like this:

http://www.google.com/imgres?q=triangle+bisected&u...

Thanks =)

### 3 Answers

- Pramod KumarLv 710 years agoFavorite Answer
Refering to the diagram provided by you. We have to prove that ∠ ACD + ∠ CBD = 90 degree

We have ---

CD is perpendicular Bisector of AB. hence any point on CD must be equidistant from A and B.

=> CA = CB

=> ∠ CAB = ∠ CBD = x (say)

Considering Triangle ACD we have ∠ CDA = 90 degree. ( given )

Hence ∠ CAD + ∠ ACD = 90 degree

=> ∠ CBD + ∠ ACD = 90 degree

Hence Proved

>>>>>>>>>>>>>>>>>

- Anonymous10 years ago
CD = CD (for obvious reasons).

AD = DB because it was bisected by CD and bisectors cut things in half so they are the same size.

CD is also perpendicular to AB (given). The two angles created are both 90 degrees.

By side-angle-side, the triangles are similar.

angle ACD corresponds to angle DCB.

It's a triangle so all the angles in triangle DCB must add up and you already know that angle CDB is 90 degrees (because CD is perpendicular to AB)

- 10 years ago
since cd is perpendicular to ab and segment CD bisects segment AB, ac = bc so the angle

CAD is = to the angle CBD

look at the triangle ADC, the angle ADC = 90 that means that the angles CAD and ACD add up to 90

since The angle CAD = the angle CBD that means that the angles CBD and ACD add up to 90