Question

Triangle a'b'c' is the result of dilating triangle abc about point p by a scale factor of 1/4. Determine whether each claim about the properties of triangle abc and triangle a'b'c' is true or false. The lengths of ab and a'b' are _________. The measures of 1) equal, equal

2) equal, not equal
3) not equal, equal
4) not equal, not equal

Answer 1

The lengths of AB and A'B' are not equal due to the dilation factor of 1/4, whereas the angle measures of triangle ABC and triangle A'B'C' are equal.

Step-by-step explanation:

The lengths of AB and A'B' are not equal; this is because the dilation factor is 1/4, meaning the lengths in triangle A'B'C' are a quarter of the corresponding lengths in triangle ABC. When a figure is dilated with a scale factor, each linear dimension of the figure is multiplied by the scale factor, and the corresponding angles remain equal. Therefore, the measures of the angles of triangles ABC and A'B'C' will be equal, but the lengths of corresponding sides will not equal.