Question

Answer the following questions below.

1) When you copy a figure at a certain scale factor how does this affect the new measurements?
2) How can you determine if two shapes are similar by looking at the rule for producing specific coordinates for the image?
3) What types of coordinate rules produce similar figures? Non-similar figures?
4) How can you decide whether or not two shapes are similar?
5) How can you use scale factors to draw similar figures or to find missing side lengths in similar figures?
6) How can you use similar triangles to find a distance that is difficult to measure directly?
7) What information does the ratio of adjacent side lengths within a rectangle give you?
8) For a pair of triangles, if the measures or corresponding angles are equal, how can you use ratios to determine if the triangles are similar?
9) If 2 shapes are similar, how can you use information about the angles to find unknown side lengths, areas, and perimeters?
10) How can you use similar triangles to estimate the heights of tall objects?

Answer 1

1) Scale factor multiplies all measurements. 2) Similar shapes have proportional coordinates. 3) Coordinates scaled by a factor for similarity. 4) Similar if angles are equal, sides proportional. 5) Scale factors resize figures proportionally. 6) Similar triangles help measure distances. 7) Ratio of adjacent sides in rectangle: tangent. 8) Equal corresponding angles, similar with ratios. 9) Similar shapes have proportional sides. 10) Estimate heights using similar triangles.

1) When copying a figure at a certain scale factor, all measurements (lengths, angles) are multiplied by that factor.

2) If the coordinates of the vertices are multiplied by the same factor to produce the new coordinates, the shapes are similar.

3) Coordinates scaled by a factor produce similar figures. Non-similar figures have different scaling factors for corresponding coordinates.

4) Two shapes are similar if their corresponding angles are equal, and their sides are proportional.

5) Scale factors are used to enlarge or reduce figures proportionally. Ratios of corresponding side lengths can help find missing lengths.

6) Similar triangles help measure distances indirectly using proportions and known distances.

7) The ratio of adjacent side lengths in a rectangle gives the tangent of the adjacent angle.

8) If corresponding angles are equal, ratios of corresponding side lengths can determine if triangles are similar.

9) Similar shapes have proportional side lengths; ratios of sides help find unknown lengths, areas, and perimeters.

10) By creating similar triangles using the object and its shadow, the height of tall objects can be estimated using known measurements and proportions.