15, 13, 14, 12, 11, 5, 8 for the other side

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Ответ:

nunezjazmine01

09.02.2022

Mathematics

The triangles $\triangle ABC \cong \triangle EDF$ by SSS congruence.

Step-by-step explanation:

Given triangle ABC with coordinates:

$A(0,0)\\B(2, 4)\\C(0,2)$

and triangle DEF with coordinates:

$D(2,0)\\E(4, 4)\\F(4,2)$

$\angle C = \angle F = 135^\circ\\\angle B = \angle D = 30^\circ$

To find:

To name the congruent triangles and the reason.

Solution:

First of all, let us find all the sides of the given triangles.

We can use distance formula to find the distance between two points ( x_1, y_1 ) and ( x_2, y_2 ).

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AB = \sqrt{(2-0)^2+(4-0)^2}\\\Rightarrow AB = \sqrt{20}\ units$

$BC = \sqrt{(0-2)^2+(2-4)^2}\\\Rightarrow BC = \sqrt{8}\ units$

$AC = \sqrt{(0-0)^2+(2-0)^2}\\\Rightarrow AC =2\ units$

$DE = \sqrt{(4-2)^2+(4-0)^2}\\\Rightarrow DE = \sqrt{20}\ units$

$EF = \sqrt{(4-2)^2+(4-4)^2}\\\Rightarrow EF = 2\ units$

$DF= \sqrt{(4-2)^2+(2-0)^2}\\\Rightarrow DF =\sqrt8\ units$

AB = DE,

AC = EF and

BC = DF

So, the triangles $\triangle ABC \cong \triangle EDF$ by SSS congruence.

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