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2 years ago

Prove that the diagonals of a parallelogram bisect each other

Mathematics

1 answer:

Nady [450]2 years ago

5 0

Answer:

[ See the attached picture ]

The diagonals of a parallelogram bisect each other.

✧ Given : ABCD is a parallelogram. Diagonals AC and BD intersect at O.

✺ To prove : AC and BD bisect each other at O , i.e AO = OC and BO = OD.

Proof : $\begin{array}{ |c| c | c | } \hline \tt{SN}& \tt{STATEMENTS} & \tt{REASONS}\\ \hline 1& \sf{In \: \triangle ^{s} \:AOB \: and \: COD } \\ \sf{(i)}& \sf{ \angle \: OAB = \angle \: OCD\: (A)}& \sf{AB \parallel \: DC \: and \: alternate \: angles} \\ \sf{(ii)} &\sf{AB = DC(S)}& \sf{Opposite \: sides \: of \: a \: parallelogram} \\ \sf{(iii)} &\sf{ \angle \: OBA= \angle \: ODC(A)} &\sf{AB \parallel \:DC \: and \: alternate \: angles} \\ \sf{(iv)}& \sf{ \triangle \:AOB\cong \triangle \: COD}& \sf{A.S.A \: axiom}\\ \hline 2.& \sf{AO = OC \: and \: BO = OD}& \sf{Corresponding \: sides \: of \: congruent \: triangle}\\ \hline 3.& \sf{AC \: and \: BD \: bisect \: each \: other \: at \: O}& \sf{From \: statement \: (2)}\\ \\ \hline\end{array}. Proved ✔$

♕ And we're done! Hurrayyy! ;)

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Write the equation of the line that passes through (-3,6) with a slope of -2

Ksenya-84 [330]

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$\diamond\large\blue\textsf{\textbf{\underline{Given question:-}}}$

What is the equation of the line that passes through (-3, 6) and has a slope of -2?

$\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond$

First, we need to write the equation of the line in point-slope form:-

$\sf{y-y_1=m(x-x_1)}$

Replace y1 with 6, m with -2, and x1 with -3:-

$\sf{y-6=-2(x-(-3)}$

On simplification,

$\sf{y-6=-2(x+3)}$

On further simplification,

$\sf{y-6=-2x-6}$

Add 6 on both sides:-

$\it{y=-2x}$

<h3>Good luck with your studies.</h3>

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6 0

1 year ago

The table of values shown below represents a linear function. Which of these points could also be an ordered pair in the table,

bearhunter [10]

Answer:

(b) (18, 27), because the rate of change of the function is 4/3

hope this helps!

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

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)