Question

practice finding areas of triangles in the coordinate plane. which statement is true of the right triangles abc and def? area of abc is greater than area of def area of abc is less than area of def area of abc is equal to the area of def there is not enough information to compare the areas of triangles abc and def

Explanation:

Step1: Recall area formula for right - triangle

The area formula for a right - triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Analyze triangle ABC

For right - triangle $ABC$, assume the base $b_1$ and height $h_1$. By counting the grid units, if we assume the horizontal side as the base and the vertical side as the height. Let's say the base $b_1 = 8$ units and the height $h_1=6$ units. Then $A_{ABC}=\frac{1}{2}\times b_1\times h_1=\frac{1}{2}\times8\times6 = 24$ square units.

Step3: Analyze triangle DEF

For right - triangle $DEF$, assume the base $b_2$ and height $h_2$. By counting the grid units, if the horizontal side is the base and the vertical side is the height. Let's say the base $b_2 = 6$ units and the height $h_2 = 8$ units. Then $A_{DEF}=\frac{1}{2}\times b_2\times h_2=\frac{1}{2}\times6\times8=24$ square units.

Answer:

Area of ABC is equal to the area of DEF