Question

Mahmoud transforms a triangular picture by using a translation and a dilation. The original picture has two angle measures of _______ and _______. The side between these two angles is _______ cm. If Mahmoud enlarges the picture so that the side between the two given angles becomes 28 cm, the scale factor of the dilation must be _______. The measure of the third angle in the original picture is _______ and the measure of the corresponding angle in the enlarged picture is _______.

Answer 1

To find the scale factor of the dilation, divide the length of the enlarged side by the length of the original side. The measure of the corresponding angle in the enlarged picture is the same as the measure of the original angle.

Step-by-step explanation:

To find the angle measures and side length of the original triangular picture, we need more information. However, we can determine the scale factor of the dilation. The problem states that Mahmoud enlarges the picture so that the side between the two given angles becomes 28 cm. Let's call the original side length of that side x cm. Since the dilation increases the length to 28 cm, the scale factor must be 28 cm divided by x cm. This can be simplified to 28/x.

The measure of the third angle in the original picture can vary depending on the angles of the given side. However, the measure of the corresponding angle in the enlarged picture will be the same as the measure of the original angle because dilations do not change angle measures.