Question

Which triangle defined by the given points on the coordinate plane is similar to the triangle illustrated? A) (2, -2)(7, -2)(2, 5) B) (2, -2)(8, -2)(2, 5) C) (2, -2)(7, -2)(2, 6) D) (2, -2)(8, -2)(2, 6)

Answer 1

The Coordinates of the given triangles are  A) (2, -2)(7, -2)(2, 5)  B) (2, -2)(8, -2)(2, 5)   C) (2, -2)(7, -2)(2, 6)      D) (2, -2)(8, -2)(2, 6) .

Using distance formula between two points we can find the length of sides of the triangle.

Distance between $(x_{1},y_{1}) and (x_{2},y_{2})=\sqrt{(x_{2}-x_{1})^2+(y_2-y_1)^2$

The two triangles are similar by following criterion

1.AA or AAA  2.SSS  3. SAS  Where A=angle ,S=side, Sides must be proportional

In  the four triangles given neither two of them  satisfies the above criteria .

So No two of them are similar to each other.  

Answer 2

The Coordinates of the given triangles are  A) (2, -2)(7, -2)(2, 5)  B) (2, -2)(8, -2)(2, 5)   C) (2, -2)(7, -2)(2, 6)      D) (2, -2)(8, -2)(2, 6) .

Using distance formula between two points we can find the length of sides of the triangle.

Distance between

The two triangles are similar by following criterion

1.AA or AAA  2.SSS  3. SAS  Where A=angle ,S=side, Sides must be proportional

In  the four triangles given neither two of them  satisfies the above criteria .

So No two of them are similar to each other.  

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