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Vlad1618 [11]
3 years ago
6

Given: vu=st, sv=tu prove vx=xt

Mathematics
1 answer:
babymother [125]3 years ago
6 0
Given <span>vu=st, sv=tu 

</span>STUV is a parallelogram :  If both pairs of opp. sides of a quad. are , then the quad is a parallelogram.

VX, XT = The diagonals of a parallelogram bisect each other.


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Triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC
e-lub [12.9K]

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Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

so

<em>In the right triangle ABM</em>

Applying the Pythagorean Theorem

BM^2=AB^2-AM^2

we have

AB=5\ units\\AM=x\ units

substitute

BM^2=5^2-x^2

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Applying the Pythagorean Theorem

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substitute

BM^2=7^2-(9-x)^2

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BM^2=49-81+18x-x^2

BM^2=-x^2+18x-32 ----> equation B

equate equation A and equation B

-x^2+18x-32=25-x^2

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18x=25+32\\18x=57\\\\x=\frac{57}{18}

Simplify

x=\frac{19}{6}

<em>Find the length of DC</em>

DC=AC-2x

substitute the given values

DC=9-2(\frac{19}{6})

DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units

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