Math / Geometry

QuestionVame: Core:
Study Guide for Test 3: Stretching and Shrinking From Investigation 1 , you should be able to... Define scale factor -
Find the scale factor between two similar figures 1. 2. Identify corresponding sides and angles (highlight one example of each in the figures above) List the similarity rules (there should be 5!)

Studdy Solution

STEP 1

1. The problem involves understanding the concept of scale factor and similarity in geometry.
2. The figures mentioned are similar, meaning they have the same shape but different sizes.
3. The task involves defining a scale factor, finding it between figures, identifying corresponding sides and angles, and listing similarity rules.

STEP 2

1. Define the scale factor.
2. Find the scale factor between the given similar figures.
3. Identify corresponding sides and angles in the figures.
4. List the similarity rules.

STEP 3

Define the scale factor:
The scale factor is the ratio of the lengths of corresponding sides of similar figures. It describes how much one figure is enlarged or reduced compared to another.

STEP 4

Find the scale factor between the given similar figures:
For the triangles, compare the corresponding sides: - Side 1: $\frac{2.5}{2} = 1.25$ - Side 2: $\frac{1}{5} = 0.2$
For the rectangles, compare the corresponding sides: - Side 1: $\frac{8.75}{5} = 1.75$ - Side 2: $\frac{5.25}{3} = 1.75$
Note: The scale factor should be consistent across all corresponding sides for figures to be similar.

STEP 5

Identify corresponding sides and angles in the figures:
For triangles: - Corresponding sides: $2$ and $2.5$ , $5$ and $1$ - Corresponding angles: Angles opposite these sides are corresponding.
For rectangles: - Corresponding sides: $5$ and $8.75$ , $3$ and $5.25$ - Corresponding angles: All angles in rectangles are $90^\circ$ .

STEP 6

List the similarity rules:
1. AA (Angle-Angle) Similarity: Two figures are similar if two angles of one figure are congruent to two angles of another.
2. SSS (Side-Side-Side) Similarity: Two figures are similar if the corresponding sides are in proportion.
3. SAS (Side-Angle-Side) Similarity: Two figures are similar if two sides are in proportion and the included angle is congruent.
4. Corresponding sides of similar figures are proportional.
5. Corresponding angles of similar figures are congruent.

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