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In the figure given identify the congruent and/or similar triangles and find the value of x and y?

Answer 1

Avery Allen

See explanation.

From the information about side lengths we can see that all angles are right angled and isosceles. we can say that:

#|EF|=2|DB|#, so the scale of simmilarity is #k=2#

Now we know that: #|DF|=2|DC|#. Since #|DF|+|DC|=3x#, we have: #|DF|=x# and #|CD|=|BD|=2x#

To calculate #x# we use the Pythagorean theorem for triangle #BCD#

#(2x)^2+ (2x)^2=(4sqrt(18))^2#

#4x^2+4x^2=16*18#

#8x^2=16*18#

#x^2=36=> x=6#

Now w euse the Pythagorean theorem for #DEF# to calculate #y#

#6^2+6^2=y^2#

#y^2=72=>y=6sqrt(2)#

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Answer 2

Jayden Jackson

To identify congruent or similar triangles in the given figure, examine angles and side lengths. Then, use properties of similar triangles to find the values of x and y.

Once the congruent or similar triangles are identified, set up ratios of corresponding sides and solve for the unknown variables using proportionality.

Please provide the figure or specific details of the triangles in question to proceed with finding the values of x and y.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.