Question

Create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem.

Answer 1

For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

How can the distance formula prove SSS Triangle Congruence Theorem?

Given that the distance formula =

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

Let say that Angle ABC has the vertices of A (-4, -2),  B (-5,1). C (0,2) and Angle DEF   has the vertices of D (7, -4), E (4,-5), F (3,0)

So lets prove it:

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

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

=$\sqrt{32}$

= 4$\sqrt{2}$

Do the same for DF:

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

= $\sqrt{(7-3)^2 + (-4-0)^2}$

=$\sqrt{32}$

= 4$\sqrt{2}$

Looking at the above, one can see the values are the same and as such this proves that AC is the same to DF. If you do the same for the other part of the angles, you will see that they are congruent.

Therefore, For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

Learn more about congruent Angle from

brainly.com/question/2938476

#SPJ