Question

The figure below shows a trapezoid, ABCD, having side AB parallel to side DC. The diagonals AC and BD intersect at point O.


ABCD is a trapezoid with DC parallel to AB. Diagonals AC and DB intersect at point O.

If the length of AO is double the length of CO, the length of BO is

half of the length of AB
double the length of DO
one-fourth the length of AC
equal to the length of AO

Answer 1

Since both of the triangles in the trapezoid are similar triangles, we can assume that they are proportionate, meaning that the correct answer would be: double the length of DO. Since they are similar.

Answer 2

thank you, can you help me with more?

Answer 3

@duckerstar146

Answer 4

Of course!

Answer 5

thank you!!

Answer 6

The figure shows three right triangles. Triangles PQS, QRS, and PRQ are similar.

Theorem: If two triangles are similar, the corresponding sides are in proportion.

Figure shows triangle PQR with right angle at Q. Segment PQ is 4 and segment QR is 9. Point S is on segment PR and angles QSP and QSR are right angles.

Using the given theorem, which two statements help to prove that if segment PR is x, then x2 = 97?

Segment PR • segment PS = 16
Segment PR • segment SR = 36
Segment PR • segment PS = 36
Segment PR • segment SR = 81
Segment PR • segment PS = 16
Segment PR • segment SR = 81
Segment PR • segment PS = 81
Segment PR • segment SR = 16

Answer 7

Ok, let's first start by finding PR: Which is....

Answer 8

uhhhhh, im not really sure, i suck at math

Answer 9

Sorry, my internet bugged out for a second, lol, anyways, we can first tell that the square root of 97 is PR, If you have any questions, I'll be here

Answer 10

So PR = Square Root of 97

Answer 11

ok thank you!!

Answer 12

Next, we have to set up proportions to find PS

Answer 13

Let PS be the variable x, and so SR = sqrt(97) - x

Answer 14

is that it?

Answer 15

Well not yet, next, we have to find two pairs of equal angles, to set up ratios on both of their sides

Answer 16

oohhhh

Answer 17

We can use PS/PQ = PQ/PR

Answer 18

okay, i tried solving it, is it C?

Answer 19

Correct!

Answer 20

YAYYY, so it is

Segment PR • segment PS = 16
Segment PR • segment SR = 81

Answer 21

Yes it is

Answer 22

thank you!!

Answer 23

No Problem