Respuesta :
sides areTriangle ABC: A(-1,3); B(-1,-3); C(-6, 0)
using distance formula
[tex]d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1_{}_{})^2}[/tex]Substitute the points and we can get
Distance of A and B is 6
Distance of A and C is 5.83
Distance of B and C is 5.83
Since two sides are equal, the triangle is an isosceles
Triangle DEF: D: (4,4); E(6,2); F(1,-3)
using distance formula
[tex]d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1_{}_{})^2}[/tex]Substitute the points and we can get
Distance of D and E is 2.83 (square root of 8)
Distance of D and F is 7.62 (square root of 58)
Distance of E and F is 7.07 (square root of 50)
Since it is not conclusive what type of triangle this is. We will use Pythagorean to check if this is a right triangle. since this theorem work on right triangles.
[tex]c^2=a^2+b^2[/tex]Using the calculated lengths/distances
the longest is set to hypotenuse
[tex](\sqrt[]{58})^2=(\sqrt[]{50})^2+\text{ }(\sqrt[]{8})^2[/tex]Since the triangle DEF follows Pythagorean theorem. It is a right triangle.
Triangle JKL: J: (8,6); K:(1,0); L:(0,2)
using distance formula
[tex]d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1_{}_{})^2}[/tex]Substitute the points and we can get
Distance of J and K is square root of 85
Distance of J and L is square root of 80
Distance of K and L is square root of 5
Since it is not conclusive what type of triangle this is. We will use Pythagorean to check if this is a right triangle. since this theorem work on right triangles.
[tex]c^2=a^2+b^2[/tex]Using the calculated lengths/distances
the longest is set to hypotenuse
[tex](\sqrt[]{85})^2=(\sqrt[]{80})^2+\text{ }(\sqrt[]{5})^2[/tex]Since the triangle JKL follows Pythagorean theorem. It is a right triangle.
Triangle RST: R:(-2,6); S(6, 2); T(-3,3)
using distance formula
[tex]d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1_{}_{})^2}[/tex]Substitute the points and we can get
Distance of R and S is square root of 80
Distance of R and T is square root of 10
Distance of S and T is square root of 82
Since it is not conclusive what type of triangle this is. We will use Pythagorean to check if this is a right triangle. since this theorem work on right triangles.
[tex]c^2=a^2+b^2[/tex]Using the calculated lengths/distances
the longest is set to hypotenuse
[tex](\sqrt[]{82})^2=(\sqrt[]{80})^2+\text{ }(\sqrt[]{10})^2[/tex]Since the triangle RST does not follow Pythagorean theorem. It is a scalene triangle. No sidesare equal. no angles are equal
