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.



Which of these is a step that can be used in the proof?

Answer 1

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1008_20/image0024e8dab25.jpg

Answer 2

@Mertsj

Answer 3

@jim_thompson5910

Answer 4

@experimentX

Answer 5

plz help

Answer 6

I would help you but I can't see the picture. It won't let me on.

Answer 7

how should i post it then?

Answer 8

i just clicked copy image address

Answer 9

Well, I'm not sure. Perhaps copy and paste it in something you can post.

Answer 10

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1008_20/image0024e8dab25.jpg

Answer 11

better?

Answer 12

@Mertsj

Answer 13

Do we have choices? All radii of a circle are equal comes to mind as one statement that might be in the proof.

Answer 14

Statement: Triangle ODS is congruent to triangle OBT.
Reason: ASA triangle congruency principle.

Statement: Triangle ODS is congruent to triangle OBT.
Reason: Hypotenuse-leg triangle congruency principle.

Statement: Angle SOD is congruent to angle TOB.
Reason: Vertically opposite angles are congruent.

Statement: Angle OSD is congruent to angle OTB.
Reason: Corresponding angles of congruent triangles are congruent.

Answer 15

The second one.

Answer 16

what makes that more correct than number one?

Answer 17

@Mertsj

Answer 18

The reason given. How are you going to get angle-side-angle congruency for those two triangles?

Answer 19

lols ok nvm im just not thinking

Answer 20

can i post another?

Answer 21

Yes.

Answer 22

Look at the figure and the conditional statement based on it.



If angle AXO is 23° and angle BXO is 44°, then angle AOB is 134°.

Samantha wrote a two column proof as shown.

Answer 23

Statement
Reason
1.
Measure of angle AXO = 23°
Measure of angle BXO = 44°
Given
2.
Segment AO is congruent to segment XO.
Segment BO is congruent to segment XO.
Radii of the same circle are equal.
3.
Triangle AOX is isosceles.
Triangle BOX is isosceles.
If two sides of a triangle are congruent, then the triangle is isosceles.
4.
Measure of angle XAO = 23°
Measure of angle XBO = 44°
The base angles of an isosceles triangle are congruent.
5.
Measure of angle XOA = (180°– 2 x 23°) = 134°
Measure of angle XOB = 2 x 23° + 44° = 90°
The sum of the interior angles of a triangle is 180°.
6.
Let measure of angle AOB be w°
Then w + 134 + 92 = 360
The sum of angles around a point is 360°.
7.
w = 360 – 226 = 134
Therefore measure of angle AOB is 134°.

Answer 24

@Mertsj

Answer 25

She made an error in statement 5. Measure of angle XOB = (180°– 2 x 44°) = 92°.

She wrote an incorrect reason for statement 6. She should have written the sum of linear pair of angles is 180°.

She wrote an incorrect reason for statement 5. She should have written the sum of the base angles of an isosceles triangle is 90°.

She made an error in statement 5. Measure of angle XOA = 90° + 44° = 134°.

Answer 26

Are those the choices?

Answer 27

the last post... yeah

Answer 28

If so, it's the first one.

Answer 29

ok...arent you supposed to explain it..

Answer 30

I don't know. I thought it was multiple choice. What do the directions say?

Answer 31

no i mean on open study i thought they did like people just giving answers like that lol...

Answer 32

ik you dont want to explain in elaborate detail, but can i be sure this is right?

Answer 33

@Mertsj

Answer 34

You mean this last one? Do you see that those two angles are for sure 44 degree?

Answer 35

yeah

Answer 36

2?

Answer 37

Because clearly angle XOB is 180-88 which is 92. Can you see that?

Answer 38

oh wait

Answer 39

So the statement in the proof about angle XOB is obviously incorrect.

Answer 40

i wasnt paying attention

Answer 41

i understand

Answer 42

Well sometimes you aren't thinking and sometimes you aren't paying attention. There is no extra charge for either. lol

Answer 43

ok thx