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**kayla1dance****Member**- Registered: 2018-01-10
- Posts: 38

Hello,

I have some questions about proofs.

#4: A square has two diagonals.

AGiven

B unfounded

C definition of an octagon

DThe number of diagonals is (n-3)n/2, where n is the number of sides, which is 4 for a square.

E 1267200 inches

F Definition of supplementary angles

I put B originally and it was wrong. I believe the correct answer is A.

12. In a triangle, if I have two angles that add up to 50 degrees, the remaining angle must be 130 degrees.

AGiven

B unfounded

C Definition of supplementary angles

DSum of angles in a triangle

E Definition of triangle inequality

F Definition of radius

I put C originally and it was wrong. I believe the correct answer is D.

14. If a central angle is 30 degrees, then the arc it defines is also 30 degrees.

AGiven

BDefinition of an inscribed angle

C unfounded

D Properties of a central angle

E Properties of an arc

F Definition of radius

I originally put C and it was wrong. I believe the correct answer is E.

17. If a circle has a central point M, and both point A and point D are on the circle, then ls_MA and ls_MD will be equal.

AGiven

B unfounded

C Definition of a line segment

D Definition of supplementary angles

E Definition of a bisector

F Definition of radius

I originally put A, but it was wrong. I believe the correct answer is F or B.

Thank you for all the help,

Kayla

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,322

Hi Kayla,

I am trying to reply on a Kindle so I am a bit limited.

The usual definition of a square is a four sided polygon with all angles and sides equal. So anything to do with diagonal must be provable from properties of the shape. If the polygon is convex, ie. no reflex angles, then if it has n sides you can draw n minus 3 diagonal from any vertex (that is n less the neighbouring points and the vertex itself) So with n vertices that's n(n-3) altogether. Except every diagonal gets counted twice as It gets counted once for one end and then again for the other end. So that formula is the reason.

The angles of a triangle add up to 180, so that explains that one.

I am unsure about the angle/arc question. This is not a part of Euclidean geometry that I have met. Either D or E I think.

These sound like radius lines to me.

Hope that is some help,

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**kayla1dance****Member**- Registered: 2018-01-10
- Posts: 38

Hello,

#4: So, is the correct answer D, because each diagonal gets counted twice instead of once. Is that why there are 4 diagonals and not 2?

#12: Yes, the angles do add up to 180 degrees and that is why I originally put C. Do you also think the correct answer is D?

#14: Okay, I will try E and I will let you know if that is correct.

#17: So, the new answer is F?

Sorry for the confusion,

Kayla

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,322

Q4' Yes. The explanation says sides=4, so diagonal = 1 x 4 / 2 = 2

Q12. I see why you thought supplementary at first but supplementary only applies to a pair of angles and this is about a triangle. D is correct.

Q17' I agree.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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