Question

Change ∆ABC by moving point B to set m∠BCA to the values in the table. Calculate and record the areas listed in the table for each measure of ∠BCA.

a) Omitting the defect area
b) Including the defect area
c) Varying based on ∠BCA
d) Constant for all ∠BCA

Answer 1

The area of triangle ABC can vary based on the measure of angle BCA.

Step-by-step explanation:

When changing the angle ∠BCA in triangle ABC by moving point B, the area of the triangle can vary based on the angle. Let's look at each part of the question:

a) Omitting the defect area: The defect area refers to the excess or shortfall in the area of the triangle compared to a perfect triangle. By omitting the defect area, we are considering the area of the perfect triangle, which can be calculated using the formula ½ * base * height.

b) Including the defect area: Including the defect area means taking into account the excess or shortfall in the area of the triangle compared to a perfect triangle. This can be calculated by subtracting or adding the defect area to the formula for the area of a perfect triangle.

c) Varying based on ∠BCA: The area of the triangle can vary based on the measure of angle ∠BCA. This is because the base and height of the triangle change as the angle changes, resulting in different areas.

d) Constant for all ∠BCA: The area of the triangle is not constant for all angles. It varies based on the measure of angle ∠BCA.