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3 years ago

How to do geometry proofs I believe it's the subtraction property

Mathematics

1 answer:

notsponge [240]3 years ago

8 0

Hi there!
You need to prove that line segment DE ≅ GH.

You're given:
Line segment DJ ≅ line segment GJ;
E is the midpoint of line segment DF;
H is the midpoint of line segment GJ.

You can justify that line segment DE ≅ line segment GH with the midpoint definition, which is a point on a line segment that divides it into two equal parts. The two equal parts in this case are line segments DE and GH, so DE ≅ GH.

Please comment with <em></em>any questions!

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Find the equation of the line that passes through the point of intersection of x + 2y = 9 and 4x -2y = -4 and the point of inter

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Answer:

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Step-by-step explanation:

The point of intersection of

$x+2y=9...eqn1$

and

$4x-2y=-4...eqn2$

is the solution of the two equations.

We add equation (1) and equation(2) to get,

$x+4x+2y-2y=9+-4$

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$\Rightarrow x=1$

We put $x=1$ into equation (1) to get,

$1+2y=9$

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$\Rightarrow y=4$

Therefore the line passes through the point, $(1,4)$ .

The line also passes through the point of intersection of

$3x-4y=14...eqn(3)$

and

$3x+7y=-8...eqn(4)$

We subtract equation (3) from equation (4) to obtain,

$3x-3x+7y--4y=-8-14$

$\Rightarrow 11y=-22$

$\Rightarrow y=-2$

We substitute this value into equation (4) to get,

$3x+7(-2)=-8$

$3x-14=-8$

$3x=-8+14$

$3x=6$

$x=2$

The line also passes through

$(2,-2)$

The slope of the line is

$slope=\frac{4--2}{1-2} =\frac{6}{-1}=-6$

The equation of the line is

$y+2=-6(x-2)$

$y+2=-6x+12$

$y=-6x+10$ is the required equation

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