Question

Complete the coordinate proof. Answer choices are on the bottom.

Answer 1

Given:

There are given that the triangle, ABC.

Where:

`\begin{gathered} A=(3,6) \\ B=(5,0) \\ C=(1,0) \end{gathered}`

Step-by-step explanation:

According to the question, we need to prove that the isosceles triangle:

So,

From the concept of the isosceles triangle:

The isosceles triangle is defined when two sides of the length of any triangle are equal.

Then,

First, we need to find the length of the sides by using the distance formula:

So,

`\begin{gathered} AB=√((x_2-x_1)^2+(y_2-y_1)^2) \\ AB=√((5-3)^2+(0-6)^2) \\ AB=√((2)^2+(-6)^2) \\ AB=√(4+36) \\ AB=√(40) \end{gathered}`

Then,

`\begin{gathered} AC=√((x_2-x_1)^2+(y_2-y_1)^2) \\ AC=√((1-3)^2+(0-6)^2) \\ AC=√((-2)^2+(-6)^2) \\ AC=√(4+36) \\ AC=√(40) \end{gathered}`

And,

`\begin{gathered} CB=√((5-1)^2+(0-0)^2) \\ CB=√((4)^2+0) \\ CB=4 \end{gathered}`

Final answer:

Hence, the step and values of the sides are shown below;

`\begin{gathered} CA=d \\ AB=d \end{gathered}`

And,

The side CA and AB is congruence by the definition of h

And,

Triangle ABC is an isosceles triangle by the the defination of b.