Given :
Four points A(2,9) , B(7,9) , C(-3,-5) and D(-3,1) .
To Find :
Are AB and CD congruent .
Solution :
Two line segment are congruent when their length is equal .
Now , length of line segment with points (a,b) and (c,d) .
.
So , length of AB is :
Also , length of CD is :
Since , length of AB and CD is not equal .
Therefore , the line segment AB and CD are not congruent .
Answer: " x = 12 " .
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Step-by-step explanation:
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<u>Note</u>: If 2 (two) triangles are "similar" ; then their corresponding sides are "proportional".
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Since one of the sides [the "hypotenuse"] of one the triangles given ; shows the measurement containing an expression with a value of "x" — specifically; " 6x + 28 " ;
→ And since we want to solve for the value of "x" ; we use this "hypotenuse" of said particular triangle to set up a "proportion" with corresponding sides; so we can solve for "x" :
→ Set up proportions as a "ratio" ; or fraction:
→ 7:28::25:(6x + 28) ; Solve for "x" ;
Let us write this in the form of a "fraction" :
→ ;
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<u>Note</u>:
→ Rewrite: " " ; by simplifying to:
" " ;
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→ Since: " " ;
= " (7÷7) / (28÷7) " ;
= " (1 /4) " ;
= " " .
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Now, rewrite the "proportion" ; as follows:
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;
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Now: "Cross multiply" ; that is:
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→ Given: " " ;
and: " b0 " ; " d
0 " ;
→ Then: " a * d " = " b * c " .
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Likewise: " 1(6x + 28) = (4) * (25) " ;
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SImplify: " 6x + 28 = 100 " ; Solve for "x" ;
→ Subtract "28" from each side of the equation:
→ " 6x + 28 - 28 = 100 - 28 " ;
to get: → " 6x = 72 " ;
Now, divide each side of the equation by: " 6 " ;
to isolate "x" on one side of the equation; & to solve for "x" ; as follows:
→ " 6x = 72 " ;
→ 6x / 6 = 72 / 6 ;
to get:
→ " x = 12 " ;
→ which is the answer.
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Hope this helps!
Best wishes in your academic pursuits
— and within the "Brainly" community!
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