determine the measure of each segment then indicate whether the statements are true or false

Answer:

[tex]d_{AB}\ne d_{JK}[/tex]

[tex]d_{AB}\ne \:d_{GH}[/tex]

[tex]d_{GH}\ne \:d_{JK}[/tex]

Therefore,

Option (A) is false

Option (B) is false

Option (C) is false

Step-by-step explanation:

Considering the graph

Given the vertices of the segment AB

Finding the length of AB using the formula

[tex]d_{AB}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

        [tex]=\sqrt{\left(2-\left(-4\right)\right)^2+\left(5-4\right)^2}[/tex]

         [tex]=\sqrt{\left(2+4\right)^2+\left(5-4\right)^2}[/tex]

         [tex]=\sqrt{6^2+1}[/tex]

         [tex]=\sqrt{36+1}[/tex]

        [tex]=\sqrt{37}[/tex]

[tex]d_{AB}\:=\sqrt{37}[/tex]

[tex]d_{AB}=6.08[/tex] units        

Given the vertices of the segment JK

From the graph, it is clear that the length of JK = 5 units

so

[tex]d_{JK}=5[/tex] units

Given the vertices of the segment GH

Finding the length of GH using the formula

[tex]d_{GH}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

         [tex]=\sqrt{\left(-2-\left(-5\right)\right)^2+\left(-2-\left(-2\right)\right)^2}[/tex]

          [tex]=\sqrt{\left(5-2\right)^2+\left(2-2\right)^2}[/tex]

          [tex]=\sqrt{3^2+0}[/tex]

           [tex]=\sqrt{3^2}[/tex]

[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]

[tex]d_{GH}\:=\:3[/tex] units

Thus, from the calculations, it is clear that:

[tex]d_{AB}=6.08[/tex]  

[tex]d_{JK}=5[/tex]

[tex]d_{GH}\:=\:3[/tex]

Thus,

[tex]d_{AB}\ne d_{JK}[/tex]

[tex]d_{AB}\ne \:d_{GH}[/tex]

[tex]d_{GH}\ne \:d_{JK}[/tex]

Therefore,

Option (A) is false

Option (B) is false

Option (C) is false

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