Question

2. Here is triangle ABC. Triangle XYZ is

similar to ABC with scale factor -

B

a. Draw what triangle XYZ might look like.

b. How do the angle measures of triangle XYZ compare to triangle ABC? Explain how

you know

c. What are the side lengths of triangle XYZ?

d. For triangle XYZ, calculate (long side) = (medium side), and compare to triangle ABC.

Answer 1

To draw triangle XYZ, use the scale factor -Ba with triangle ABC. The angle measures of XYZ are the same as ABC. To find the side lengths of XYZ, use the scale factor to determine the lengths of the corresponding sides in ABC and scale them down. Compare the long side to the medium side in XYZ by calculating the ratio of their lengths.

Step-by-step explanation:

Triangles XYZ and ABC

a) To draw triangle XYZ, we need to use the scale factor -Ba. We first draw triangle ABC and then use the scale factor to determine the corresponding points on triangle XYZ.

b) The angle measures of triangle XYZ will be the same as triangle ABC because corresponding angles of similar triangles are equal.

Side lengths of triangle XYZ

c) To find the side lengths of triangle XYZ, we can use the scale factor to determine the lengths of the corresponding sides in triangle ABC and then scale them down using the scale factor -Ba.

Comparison between Triangle XYZ and ABC

d) To compare the long side to the medium side in triangle XYZ, we need to calculate the ratio of their lengths. We can use the scale factor -Ba to find the lengths of the corresponding sides in triangle ABC and then compare them.

Answer 2

Triangle XYZ is similar to triangle ABC with a scale factor -Ba. The angle measures of triangle XYZ will be the same as triangle ABC. To find the side lengths of triangle XYZ, we multiply each side length of triangle ABC by -Ba. The ratio of the long side to the medium side in triangle XYZ can be calculated using the ratios of the corresponding sides in triangle ABC.

Step-by-step explanation:

Triangle XYZ

a. To draw triangle XYZ, we need to use the scale factor -Ba. This means that each side of triangle XYZ will be Ba times smaller than the corresponding side of triangle ABC. For example, if side AB of triangle ABC is 10 centimeters long, then side XY of triangle XYZ will be (10 * -Ba) centimeters long.

b. The angle measures of triangle XYZ will be the same as the angle measures of triangle ABC. This is because the scale factor only affects the lengths of the sides, not the angles. So if angle BAC of triangle ABC is 30 degrees, then angle YXZ of triangle XYZ will also be 30 degrees.

c. To find the side lengths of triangle XYZ, we need to multiply each side length of triangle ABC by -Ba. For example, if side AB of triangle ABC is 10 centimeters long, then side XY of triangle XYZ will be (10 * -Ba) centimeters long.

d. To calculate the ratio of the long side to the medium side in triangle XYZ, we can use the ratios of the corresponding sides in triangle ABC. For example, if the long side of triangle ABC is 20 centimeters long and the medium side is 10 centimeters long, then the ratio would be (20/10) = 2. We can then multiply this ratio by -Ba to find the corresponding ratio in triangle XYZ.