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Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two-c

natali 33 [55]

Answer: By the slope formula.

Step-by-step explanation:

Given: ABC is a triangle (shown below),

In which A≡(6,8), B≡(2,2) and C≡(8,4)

And, D and E are the mid points of the line segments AB and BC respectively.

Prove: DE║AC and DE = AC/2

Proof:

Since, And, D and E are the mid points of the line segments AB and BC respectively.

Therefore, By mid point theorem,

coordinate of D are $(\frac{2+6}{2} , \frac{2+8}{2} ) = (\frac{8}{2} , \frac{10}{2} )= (4,5)$

Coordinate of E are $(\frac{2+8}{2} , \frac{2+4}{2} ) = (\frac{10}{2} , \frac{6}{2} )= (5,3)$

By the distance formula,

$DE=\sqrt{(5-4)^2+(3-5)^2}=\sqrt{5}$

$AC=\sqrt{(8-6)^2+(4-8)^2}=2\sqrt{5}$

By the slope formula,

Slope of AC = $\frac{4-8}{8-6} = \frac{-4}{2} = -2$

Slope of DE = $\frac{3-5}{5-4} = \frac{-2}{1} = -2$

Statement Reason

1. The coordinate of D are (4,5) and 1. By the midpoint formula

the coordinate of E are (5,3)

2. The length of DE = √5 2. By the Distance formula

The length AC = 2√5 ⇒ Segment DE

is half the length of segment AC

3. The slope of DE = -2 and the 3. By the slope formula

slope of AC = -2

4. DE║AC 4. Slopes of parallel lines are equal

7 0

3 years ago

Read 2 more answers

In Cherokee County, the fine for speeding is $17 for each mile per hour the driver is traveling over the posted speed limit. In

zlopas [31]

Answer:13 miles over the speed limit

Step-by-step explanation:

3 0

3 years ago

To create an entry code, you must first choose 2 letters and then 2 single digit numbers. How many entry codes can you create?

ivann1987 [24]

Answer:

55600

Step-by-step explanation:

First times the number of possibilities of the amount of letters it could be so 26X26 as it is a non consecutive possibility that means both letters have the possibility to be the same. Then take the product of 26X26 and multiply it by the possibilities of the first number which is 10 then repeat that by again multiplying the product by 10 to represent the number of possibilities for the second number

3 0

3 years ago

PLEASE HELP NTH TERM MATHS

fredd [130]

Answer:

odd numbers

Step-by-step explanation:

4 - 7 is 3, 7 - 12 is 5, 12 - 19 is 7, 19 to 28 is 9

So just keep counting

4 0

2 years ago

Read 2 more answers

The ratio of boys to girls in the entire 6th grade is 3 to 2. Given this ratio, which two class compositions are possible?

gtnhenbr [62]

Answer:

There's an infinite number of possible answers because there might be any multiplication of 3 for boys and any multiplication of 2 for girls. So, for example:

There might be 3 boys and 2 girls.

There might be 6 boys and 4 girls.

There might be 9 boys and 6 girls.

There might be 12 boys and 8 girls.

etc...

In each case the ratio stays the same - 3 : 2.

Of course there probably can't be more than a few dozens of people in one class, but theoretically we can raise the numbers up to infinite.

Step-by-step explanation:hope this help.

7 0

3 years ago