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3 years ago

Proving the Parallelogram Side Theorem

Mathematics

1 answer:

sasho [114]3 years ago

5 0

Answer:

To prove a quadrilateral is a parallelogram, you must use one of these five ways.

Prove that both pairs of opposite sides are parallel.

Prove that both pairs of opposite sides are congruent.

Prove that one pair of opposite sides is both congruent and parallel.

Prove that the diagonals bisect each other.

Step-by-step explanation:

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Jeff gave 1/4 of a sum of money to his wife. Then he divided the remainder equally among his 4 children.

Semenov [28]

Answer:

A) The fraction of sum of money did each child receive is $\frac{3 x}{16}$

B) The sum of money did Jeff have $ 3200

Step-by-step explanation:

Given as :

Let The sum of money did Jeff have = $ x

The fraction of money did Jeff's wife get = $\frac{1}{4}$ of $ x

The remaining money Jeff will have = $ x - $\frac{1}{4}$ of $ x

I.e The remaining money Jeff will have = $\frac{4 x - x}{4}$

= $\frac{3 x}{4}$

A ) The remaining amount of money is divided equally among 4 children

So, The fraction of sum of money did each child receive = $\frac{\frac{3 x}{4}}{4}$

I.e The fraction of sum of money did each child receive = $\frac{3 x}{16}$

B ) If each child will receive $ 600

∴, $\frac{3 x}{16}$ = $ 600

Or, 3 x = $ 600 × 16

Or, 3 x = $ 9600

∴ x = $\frac{9600}{3}$

I.e x = $ 3200

So, The sum of money did Jeff have $ 3200

Hence ,

A) The fraction of sum of money did each child receive is $\frac{3 x}{16}$

B) The sum of money did Jeff have $ 3200 Answer

8 0

3 years ago

Someone help me with example plzz

kati45 [8]

Answer:

Angle JML= 132( given)

Triangle JML= 180( Angle sum property)

2x+ 48= KML( Exterior angle property)

In triangle JML,

76 + ∠L+ ∠KML=180°

∠KML=∠L( angles opposite to equal sides are equal)

76+2(2x+48)=180°

2(2x+48)=104°

2x=104-48=64°

x= 32°

Step-by-step explanation:

Hope it helps : )

5 0

3 years ago

In the chart of accounts, each account number has two digits. The first digit indicates the major account group to which the acc

Eduardwww [97]

Answer:

The correct option is (b)

Step-by-step explanation:

Chart of accounts refers to listing or arranging various accounts for the ease of locating them. Listing is done based on the order of appearance beginning with balance sheet and then income statement.

The order starts with assets, followed by liabilities and stockholders' equity from the balance sheet and revenue and expenses from income statement.

So, the correct order is stated in option (b).

4 0

3 years ago

Read 2 more answers

Find the midpoint of the line segment with the endpoints A and B.<br> A(4.8): B(10,2)

rjkz [21]

Answer:

The midpoint is ( 7,5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinate of the endpoints and divide by 2

( 4+10)/2 = 14/2 = 7

To find the y coordinate of the midpoint, add the y coordinate of the endpoints and divide by 2

(8+2)/2 = 10/2 = 5

The midpoint is ( 7,5)

6 0

3 years ago

Indicate the equation of the given line in standard form. Show all your work for full credit. the line containing the median of

alukav5142 [94]

Answer:

* The equation of the median of the trapezoid is 10x + 6y = 39

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) , (x2 , y2) is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The mid point of the line whose end point are (x1 , y1) , (x2 , y2) is

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

- The standard form of the linear equation is Ax + BC = C, where

A , B , C are integers and A , B ≠ 0

- The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

- It has two properties:

# It is parallel to both bases

# Its length equals half the sum of the base lengths

* Lets solve the problem

- The trapezoid has vertices R (-1 , 5) , S (! , 8) , T (7 , -2) , U (2 , 0)

- Lets find the slope of the 4 sides two find which of them are the

parallel bases and which of them are the non-parallel bases

# The side RS

∵ $m_{RS}=\frac{8-5}{1 - (-1)}=\frac{3}{2}$

# The side ST

∵ $m_{ST}=\frac{-2-8}{7-1}=\frac{-10}{6}=\frac{-5}{3}$

# The side TU

∵ $m_{TU}=\frac{0-(-2)}{2-7}=\frac{2}{-5}=\frac{-2}{5}$

# The side UR

∵ $m_{UR}=\frac{5-0}{-1-2}=\frac{5}{-3}=\frac{-5}{3}$

∵ The slope of ST = the slop UR

∴ ST// UR

∴ The parallel bases are ST and UR

∴ The nonparallel sides are RS and TU

- Lets find the midpoint of RS and TU to find the equation of the

median of the trapezoid

∵ The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

∵ The midpoint of RS = $(\frac{-1+1}{2},\frac{5+8}{2})=(0,\frac{13}{2})$

∵ The median is parallel to both bases

∴ The slope of the median equal the slopes of the parallel bases = -5/3

∵ The form of the equation of a line is y = mx + c

∴ The equation of the median is y = -5/3 x + c

- To find c substitute x , y in the equation by the coordinates of the

midpoint of RS

∵ The mid point of Rs is (0 , 13/2)

∴ 13/2 = -5/3 (0) + c

∴ 13/2 = c

∴ The equation of the median is y = -5/3 x + 13/2

- Multiply the two sides by 6 to cancel the denominator

∴ The equation of the median is 6y = -10x + 39

- Add 10x to both sides

∴ The equation of the median is 10x + 6y = 39

* The equation of the median of the trapezoid is 10x + 6y = 39

7 0

4 years ago