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2 years ago

How do you prove each of the following properties of a parallelogram?

Mathematics

1 answer:

Svet_ta [14]2 years ago

4 0

Step-by-step explanation:

the opposite angles are equal

i.e. i) < A = <C ii) < B = < D

the opposite sides are equal that is

i)AB =CD

ii) AD= BC

the diagonals bisect each other

i) AO=OC

ii)BO=OD

the adjacent angle are supplementary . that is

i)<D + < C=180 DEGREE

ii)<A+<D=180degree

iii)<B+<C=180 degree

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Margaret is thinking of a number. She says, “My number is odd. It is a factor of 36 and a multiple of 3” There are two possible

Novay_Z [31]

Answer:

3,9

Step-by-step explanation:

Factors of 36 = 1,2,3,4,6,9,12,18,36

Those factors which are odd = 1,3,9

Odd Factors which are multiple of 3 = 3,9

So, these are the two numbers Margret might be thinking of.

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3 years ago

You have at most $3.65 to make copies for a school project. Each copy costs $0.25. Write and solve an inequality that represents

slamgirl [31]

The equation for the problem is $0.25x$ ≤ $3.65$

Hope it helps!

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3 years ago

Find the value of b.

Nesterboy [21]

Answer: $230^{\circ$

Step-by-step explanation:

For convenience, I labeled some points as shown in the attached picture.

Also, I assume $\overline{AB}$ and $\overline{BC}$ are tangents to the circle.

$\overline{BO} \cong \overline{BO}$ (reflexive property)
$\overline{AB} \cong \overline{BC}$ (tangents drawn from a common external point are congruent)
$\angle BAO \cong \angle BCO$ (right angles are congruent)

Therefore, we know $\triangle ABO \cong \triangle CBO$ by HL.

Thus, by CPCTC,

$\angle AOB \cong \angle BOC \implies m\angle BOC=65^{\circ}\\\\\implies m\angle AOC=130^{\circ}$

This means the measure of minor arc AC is $130^{\circ}$ , and thus $b=360^{\circ}-130^{\circ}=\boxed{230^{\circ}}$

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1 year ago

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ra1l [238]

Statement 1 is correct

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3 years ago

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3 years ago