maths help !!!!!?

Question

imm going to try and explain how this triangle looks like. firstly, there is a small triangle called OCD. O is the top, C is the left and D is the right. on top of the triangle is a larger triangle called ABO. O is the top of it, but the triangle is upside down, so these 2 triangles both have O. A is the left of the upside down triangle, and B is the right of the upside down triangle.
the length of AB is 7 cm
the length of BO is 6 cm
the length of CD is 3.5cm

the question is asking that :
is AB||CD and AB = 7 cm, BO = 6cm and CD = 3.5 cm, calculate CB.
PLEASE HELP. IM STUCK!!!! i also have many more questions that i need help with, and if you can help, is there a way to help me with all of them??
ALL HELP IS GREATLY APRECIATED

Answer 1

well im not a math genius and im guessing this is geometry which i took last yr but kinda forgot. anyways is there a way to prove triangles congruent by the Angle-Angle-Angle (AAA) theorem? If so then the this is parallel. I think CB is 9 because look at AB its 7 right? then look at CD. iTS HALF OF SEVEN RIGHT? so then you do 6 divided by 2. which equals three and then you add 3 and 6 to get 9. thats how i see it. and i left out some other theorems.

Answer 2

My guess is that the triangles meet at 0, but that the lines are straight there, too? So it would be one straight line from D to A and one straight line from C to B? Then, since the same lines make angle O in both triangles in the picture, those angles are the same (congruent)

Then, because the 2 lines are parallel, by alternate interior angles, angle A and angle D are the same, and angle B and angle C are the same. By the AAA law, this makes them similar triangles.

We can use proportions to find missing lengths on similar triangles. Just match up the parts of the triangles that are the same part. So AB goes with DC and BO goes with CO

Then make a fraction for each part and set them equal

AB/DC=7/3.5 and we'll call CO x, so BO/CO=6/x
7/3.5=6/x
cross multipliy, and you get 7x=3.5*6=21
so 7x=21, and x =3

Then, to get BC, add BO and OC, which is 6 + 3 = 9

Answer 3

Because AB and CD are parallel, that means that the two triangles are similar. That simply means that the triangle has the same angles, but different lengths of sides. (Think of a slice of pizza and a smaller picture of it. Same proportions, different size.) How is this triangle similar? Angle AOB and Angle COD are the same measure because they are vertical angles. Also, Angle B and Angle C are the same, and Angle A and Angle D are the same because they are alternate interior (any of this sound familiar?)

Anyway, AB and CD are proportional. AO and OD are also proportional. As are CO and OB. All this means is that you have to set up a ratio. Since AB is 7 cm and CD is 3.5 cm, we know that Triangle ABO is twice as big as Triangle CDO. Why? Because 7 (AB's length) is 3.5 (CD's length) times 2. Since BO is 6, and is twice as big as CO, that would make CO be 3 cm. Now you know CO's length and OB's length. All you have to do is add them together to get CB's length.

Answer 4

I too share the popular feeling that diagrams must be allowed by Yahoo! I'll do my best.

You're not that clear, but IF O, A and D are collinear and so are O, B and C,

AB||CD

In triangle ABO and triangle DCO,

angle ABO = angle DCO (Alternate interior angles, AB||CD)
angle AOB = angle DOC (Vertically opposite angles)

So, ABO ~ DCO (AA similarity)

So, AB/CD = BO/CO

7/3.5 = 6/CO
6/CO = 2
CO = 3 cm.

BC = BO + OC = 6 + 3 = 9cm

So, BC = 9cm

I think we can obtain a result even if A, O and D & B, O and C are non - collinear. I'll come back and post if it is true. In the meantime, you can rely on this answer.

Answer 5

**The periods are here for spacing, nothing else.**
.A--------B
.\.........../
...\ ......./
......\../
.......O
....../..\
...../....\
..../......\
..C------D

This is your triangle. Since AD is a line and CB is a line and they go through O, angle COD and angle AOB are vertical angles, which makes them congruent. Now, since AB||CD (they are parallel), you have congruent alternate interior angles. That is, angle A is congruent to angle D and angle C is congruent to angle B. Therefore your triangles are similar. You can set up a proportion of corresponding sides.
AB....BO
---- = ------
CD....CO

so

7..........6
---- = ------
3.5.....CO
Now, cross multiply. 7*CO = 3.5*6. Solve for CO and then you can add it to OB to get the length of CB. Let me know if you get stuck. It's kind of hard to type this out. I can probably help you with more. I teach geometry.

Answer 6

can u take a pic of the prob and post it because that would really help