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kap26 [50]
3 years ago
6

Which statement correctly names the congruent triangles and justifies the reason for congruence? a coordinate plane with triangl

es ABC and FED at A 0 comma 0, B 4 comma 0, C 1 comma 3, D 5 comma 2, E 8 comma 5, and F 8 comma 1, segment AC measures 3 and 2 tenths units, angle A measures 72 degrees, segment DF measures 3 and 2 tenths units, and angle F measures 72 degrees Î"ABC ≅ Î"FDE by HL Î"ABC ≅ Î"FED by SAS Î"ABC ≅ Î"DEF by HL Î"ABC ≅ Î"DEF by SAS.
Mathematics
1 answer:
Colt1911 [192]3 years ago
7 0

Use the distance formula to justify the congruence. The correct option is B. \Delta ABC\cong \Delta FED\\.

<h3>Given, </h3>

the coordinates of \Delta ABC and \Delta FED are A(0,0)\ B(4,0)\ C(1,3)\ D(5,2)\ E(8,5)\ F(8,1).

The length of segment AC is \frac{3}{2} and the length of segment DF is also \frac{3}{2} .

\angle A = 72^{\circ} and \angle F =72^{\circ}.

We have to find the correct statement regarding the triangles to be congruent.

<h2>Distance formula</h2>

We know that, The distance formula to calculate the distance between two points ( x_{1} , y_{1}) , and ( x_{2}, y_{2}) is given as,

D=\sqrt{(x_{2}-x_{1} ) ^{2}+(y_{2} -y_{1} )^2 }

So, The distance between F(8,1) and E(8,5) Will be,

FE=\sqrt{(8-8)^2+(5-1)^2} \\FE=\sqrt{4^2} \\FE=4\\

Similarly, the distance between A(0,0) and B(4,0) will be,

AB=\sqrt{(4-0)^2+(0-0)^2} \\AB=\sqrt{4^2} \\AB=4

So, AB=FE.......(1)

Now, in \Delta ABC and \Delta FED,

AB=FE ( from equation 1 ).

\angle A=\angle F ( Given )

AC=DF ( Given )

So, By Side angle Side congruence rule,

\Delta ABC\cong \Delta FED.

Hence the correct option is B. \Delta ABC\cong \Delta FED\\.

For more details on SAS congruence rule follow the link:

brainly.com/question/11804042

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