Question

The figure shows a circle with center O and two congruent chords AB and CD. To prove that the chords are equidistant from the center, it has to be proved that segment OS is congruent to segment OT.

Answer 1

I'll give you a quick proof, and you can find the answer.

AB congruent to CD given
OA, OB, OC, OD congruent radii of a circle are all congruent
triangle ABO congruent to triangle CDO side-side-side
OS congruent to OT corresponding altitudes of congruent triangles
are congruent

Answer 2

d?

Answer 3

I'll give you a quick proof, and you can find the answer.

AB congruent to CD given
OA, OB, OC, OD congruent radii of a circle are all congruent
triangles ABO, CDO congruent side-side-side
OS congruent to OT corresponding altitudes of congruent triangles
are congruent

Answer 4

I think so.

Answer 5

wait so it is d? im confused now haha

Answer 6

My columns didn't work out as well as I had hoped (either attempt!) but you seem to have figured it out.

Answer 7

haha okay can you help me with 1 more?

Answer 8

a, b not true.
c not substantiated.
d true

Answer 9

I've got a while, go ahead.

Answer 10

okay one sec and thanks!

Answer 11

What do you think the answer is?

Answer 12

c but im not sure

Answer 13

OK, I have a question. To say that the two triangles are congruent, we have to know that the corresponding angles are the same, and the connecting segment is the same. Where do we establish that the connecting segments are the same?

Answer 14

we didnt?

Answer 15

Check below that box.....

Answer 16

Then read answer a carefully, and tell me what you think.

Answer 17

ok

Answer 18

You get it?

Answer 19

so the sequence od 3and 4 are mixed up

Answer 20

When you are doing a proof, you don't use a fact, then establish it; you establish it, then use it.

Answer 21

ohhhh got it!

Answer 22

Yeah, that's right. Answer a.

Answer 23

okay i just have one last question that im completely lost

Answer 24

I'm sorry, I haven't taught geometry in a while. Not sure how to do that one.

Answer 25

thanks anyways :)

Answer 26

Hope I was helpful. Do math every day.