SOLUTION: A, B,C, D are collinear. If BC = CD, BD = AB - 1, and AD = 9. Find AB, BC, CD and BD?

SOLUTION: A, B,C, D are collinear. If BC = CD, BD = AB - 1, and AD = 9. Find AB, BC, CD and BD?

Algebra.Com

Question 282505: A, B,C, D are collinear. If BC = CD, BD = AB - 1, and AD = 9. Find AB, BC, CD and BD?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Just so the explanation doesn't look quite so ugly with all of those capital letters that make you keep referring back to the diagram, I'm going to let

represent the value of the measure of AB. Likewise, the value of the measure of BC will be

and the value of the measure of CD will be CD. The value of the measure of AD is given as 9.

We are given that

and we can see that AD is the sum of

, so we can write:

Also, we are given that

which is to say:

Solving this little system we get

And knowing that

we can substitute

So AB = 5, BC = 4, and CD = 4, and BD must be 8.

John

RELATED QUESTIONS
Complete the following proof: 1. B is between A and D. C is between B and D. 2.... (answered by MathLover1)

1. If A, B, C, D are collinear and AB = 8, AC = 12, AD = 16, BC = 20, BD = 24, CD = 28,... (answered by ikleyn)

Let A,B,C,D be collinear points such that AB = 2, AC = 3, AD = 4, BC = 5, BD = 6, CD = 1: (answered by greenestamps)

A, B, C, D, and E are collinear points. AE = 34, BD = 16, and AB = BC = CD. What is the... (answered by josgarithmetic)

A,B,C AND ,D ARE COLLINEAR AB=CD PROVE AC=BD (answered by richard1234)

._____._________._____. A B C D Statements Reasons AC=BD (answered by midwood_trail,deanice_01@yahoo.com,smartguy101)

ABC is a triangle its perimeter is 27cm. BD ia a straight line that biscect angle B and... (answered by ikleyn)

Points A, B, C, and D are collinear and positioned in that order. Find the length... (answered by Fombitz)

Points A, B, C, D are collinear and in that order. Find the length indicated. Find BD... (answered by Alan3354)