Question

PLEASE HELP!!! GEOMETRY AND IDK WHAT IM DOING NEED TO PASS

In the diagram, and . What additional information is necessary to prove that ΔABC is similar to ΔFGH, using the SSS similarity theorem?

Answer 1

revolvelution

Explanation:

Answer 2

Answer with explanation:

To prove two triangles are similar using SSS Similarity Criterion we need to prove that sides of triangles are Proportional.

Sides of two triangles can be obtained using Distance formula.

Coordinates of ΔABC are= A(0,0) , B(6,3) and C(-3,3)

Coordinates of ΔFGH are=F(-3,-2),G(-1,-3) and H(-4, -3)

`AB=√((6-0)^2+(3-0)^2)\\\\=√(36+9)\\\\=√(45)\\\\=5√(3)\\\\BC=√((6+3)^2+(3-3)^2)\\\\BC=9\\\\AC=√((-3-0)^2+(3-0)^2)\\\\AC=√(9+9)\\\\=√(18)\\\\=3√(2)\\\\FG=√((-3+1)^2+(-2+3)^2)\\\\FG=√(4+1)\\\\FG=√(5)\\\\GH=√((-1+4)^2+(-3+3)^2)\\\\GH=3\\\\HF=√((-4+3)^2+(-3+2)^2)\\\\HF=√(1+1)\\\\HF=√(2)`

Ratio of Corresponding sides are

`1.\rightarrow (AB)/(FG)=(3√(5))/(√(5))\\\\=3\\\\2.\rightarrow (AC)/(FH)=(3√(2))/(√(2))\\\\=3\\\\3.\rightarrow (CB)/(HG)=(9)/(3)\\\\=3\\\\\rightarrow (AB)/(FG)=(AC)/(FH)=(CB)/(HG)`

As corresponding sides are proportional, so trinagles are Similar.

⇒ ΔABC ≅ ΔFGH--------[SSS]

Hence proved.