6.3 Use similar polygons

6.3 Use similar polygons

Geometry

Mrs. LaGrange

Similar Polygons

For similar polygons:

Corresponding interior angles are congruent, and corresponding sides are proportional.

Multiple Choice

Are the triangles similar?

• Yes
• No

Multiple Choice

Are the triangles similar?

• Yes
• No

Scale Factor

If two polygons are similar, then the ratio of the

lengths of two corresponding sides is called the

scale factor.

Scale Factor

If the scale factor is less than 1 (a fraction or decimal less than 1) the result is a reduction.

If the scale factor is greater than 1 the result is an enlargement.

Multiple Choice

If the scale factor is greater than one, the new figure will be

• a reduction
• an enlargement
• a scale
• not proportional

Multiple Choice

If the scale factor is less than one, the new figure will be

• an enlargement
• a reduction
• a scale factor
• bigger

Multiple Choice

The two polygons are similar. What is the scale factor of the big quadrilateral to the small quadrilateral?

• 5/4

• 4/5

• 5/2

• 2/5

Multiple Choice

The two polygons are similar. What is the scale factor of the small quadrilateral to the big quadrilateral?

• 5/4

• 4/5

• 5/2

• 2/5

The two triangles are similar. Can you solve for x?

Use proportions of corresponding sides to solve for x.

 $\frac{x}{12}=\frac{20}{16}\ \ so,\ 16x=240\ and\ x=15$  

Perimeters

The ratio of lengths in similar polygons is the same as the scale factor. Therefore, the ratio of their perimeters is the same as the scale factor.

Multiple Choice

Find the perimeter of each polygon.

• P(left∆) = 40
  P(right∆) =60
• P(left∆) = 40
  P(right∆)=65 
• P(left∆) = 45
  P(right∆) = 60
• P(left∆) = 45  ,P(right∆) =65

 

Scale Factor:

 $\frac{15}{10}=\frac{3}{2}$  
Value of x: $\frac{x}{10}=\frac{18}{15}\ \rightarrow15x=180\rightarrow x=12$  
Perimeter of ABCDE:
Perimeter of FGHJK =3/2 Perimeter of ABCDE. 
 $72=\left(\frac{3}{2}\right)P\left(ABCDE\right)\rightarrow\ \left(\frac{2}{3}\right)\left(72\right)=P\left(ABCDE\right)=48$    

Similarity and Congruence

Any two congruent figures are also similar. They have a scale factor of 1:1.

Multiple Choice

• Yes, EFGH~KLMN. Scale Factor: 2:1

• Yes, EFGH~KLMN. Scale Factor: 1:2

• No, EFGH is not similar to KLMN.

Great job!

Take-away for similar polygons:

1. Corresponding Angles are congruent.
2. Corresponding sides are proportional.
3. Scale factor is IMPORTANT!
4. Side Lengths, Perimeters, Medians, and Altitudes, of similar polygons are proportional based on the scale factor.