-Let a and b represent positive real numbers. Explain why the triangle with vertices at A(a,0), B(0,a) and C(0,0) is an isosceles right triangle.

Question

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The Answer is For For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

, we apply the Slope Formula to show that For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

or 0; thus, For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

is horizontal. Also, For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

, which is undefined; thus, For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

is vertical. Then For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

,
so

is a right triangle.
Because For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

is horizontal, its length is the positive difference is x coordinates; that is, For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

or a. Because For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

is vertical, its length is the positive difference in its y coordinates; that is, For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

or a. Then For , we apply the Slope Formula to show that or 0; thus, is horizontal. Also, , which is undefined; thus, is vertical. Then , so is a right triangle. Because is horizontal, its length is the positive difference is x coordinates; that is, or a. Because is vertical, its length is the positive difference in its y coordinates; that is, or a. Then and is also isosceles.

and

is also isosceles.

-Let a and B Represent Positive Real Numbers