The image shows two triangles, ABC and XYZ. Triangle XYZ is similar to triangle ABC with scale factor 1/4. This means that each side of triangle XYZ is 1/4 the length of the corresponding side of triangle ABC.
Side lengths:
The side lengths of triangle ABC are given as 5, 5, and 4. Therefore, the side lengths of triangle XYZ are 1.25, 1.25, and 1.
Angle measures
Since the two triangles are similar, all of their corresponding angles are equal in measure. This means that the angle measures of triangle XYZ are the same as the angle measures of triangle ABC.
Drawing triangle XYZ
To draw triangle XYZ, we can start by drawing a smaller triangle that is congruent to triangle ABC. To do this, we can simply reduce the size of triangle ABC by a factor of 1/4. Once we have drawn the smaller triangle, we can label it as triangle XYZ.
Other properties
In addition to the properties mentioned above, there are a few other things that we can say about similar triangles. For example, the ratio of the areas of two similar triangles is equal to the square of the scale factor. This means that the area of triangle XYZ is 1/16 the area of triangle ABC.
Real-world examples
Similar triangles can be found all around us in the real world. For example, if we look at a shadow of a tree, the shadow is a similar triangle to the tree itself. Another example is a map. When we make a map, we are essentially creating a similar triangle of the real world.