Triangle EFG has coordinates E(-3, 4), F(-3, -3), and G(4, -3). Triangle JKL has coordinates J(1, 1), K(-6, 1), and L(-6, -6). Use coordinate geometry to determine if these two triangles are congruent. If they are not congruent, state the reason.

They are Congruent Triangles

Step-by-step explanation:

Two figures are congruent if they have the same shape and size.

To determine if Triangle EFG and JKL are congruent, we simply find the length of the sides and do a comparison.

Triangle EFG has coordinates E(-3, 4), F(-3, -3), and G(4, -3).

Distance between two points on the coordinate plane is given by:

√[(x₁-x₂)²+(y₁-y₂)²]

In Triangle EFG,

EF=√[(-3-(-3))²+(4-(-3))²]=√[(-3+3)²+(4+3)²]=√7²=7

EG=√[(-3-4)²+(4+3)²]=√[(-7)²+(7)²]=√98=7√2

FG=√[(-3-4)²+(-3+3)²]=√(-7)²=√49=7

Therefore:

EF=7, EG=7√2 and FG=7

Also in Triangle JKL with coordinates J(1, 1), K(-6, 1), &L(-6, -6).

JK=√[(1+6)²+(1-1)²]=√(7)²=√49=7

JL=√[(1+6)²+(1+6)²]=√98=7√2

KL=√[(-6+6)²+(1+6)²]=√49=7

Therefore:

JK=7, JL=7√2 and KL=7

We can see that the length of the sides of Triangle EFG and JKL are the same. So the two triangles are congruent.

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step-by-step explanation: