Activity 4-5: Similarity of Polygons

Similar Polygons

When we use a map to plan a trip, a sketch to build a bookcase, or a pattern to sew a dress, we are working with similar figures. When polygons have the same shape but may be different in size, they are called similar polygons.

Two polygons are similar (~)

• if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.

• The order of the vertices in a similarity statement is important. It identifies the corresponding angles and the corresponding sides.

• Like congruent polygons, similar polygons may be repositioned so that corresponding parts are easy to identify

Activity 4: Similar Polygons

 Solve the following problems on similar polygons. 

Multiple Choice

I. 1. Determine whether the figures in the left are similar or not.

• SIMILAR

• NOT SIMILAR

Multiple Choice

I. 2. Determine whether the figures in the left are similar or not.

• SIMILAR

• NOT SIMILAR

Multiple Choice

I. 3. Determine whether the figures in the left are similar or not.

• SIMILAR

• NOT SIMILAR

You may check these links for more example.

https://www.youtube.com/watch?v=5TCrWjdWuQA

https://www.youtube.com/watch?v=tgFz9AfliCE

Fill in the Blanks

II. 1. The given pair of polygons are similar. Using proportions, find the values of x and y.

Write the value of x first.

Ex.: 1,2

Fill in the Blanks

II. 2. The given pair of polygons are similar. Using proportions, find the values of x and y.

Write the value of x first.

Ex.: 1,2

Fill in the Blanks

II. 3. The given pair of polygons are similar. Using proportions, find the values of x and y.

Hint: Corresponding sides are proportional and corresponding angles are congruent.

Write the value of x first.

Ex.: 1,2

Scale factor

• When you compare the lengths of corresponding sides or corresponding angles of similar figures, you usually get a numerical ratio. This ratio is called the scale factor for the two figures. Scale factors are often given for models of real-life objects.

Fill in the Blanks

III. 1. A rectangle with length 60 centimeters and height 40 centimeters is enlarged so that the new rectangle is similar to the original and the scale factor is  $\frac{1}{4}$  . Find the length and height of the new rectangle. 

Write the length first. Ex.: 20,10cm

Fill in the Blanks

III. 2.  $\Delta ABC\sim\Delta DEF$  and their scale factor is 7:9. If the perimeter of  $\Delta ABC$  is 42 cm, what is the perimeter of  $\Delta DEF$  ?

Fill in the Blanks

III. 3. Quadrilateral PQRS ~ Quadrilateral TUVW. One side of PQRS has length 12 m. The corresponding side of TUVW has length 15 m. The perimeter of TUVW is 35 m, what is the perimeter of PQRS?

Fill in the Blanks

III. 4. The areas of two similar polygons are in the ratio 64:81. Find the ratio of their corresponding sides.

Activity 5. Proving Similar Triangles

Supply the missing statements/reasons for each proof of triangle similarity by ticking all choices that apply.

Multiple Select

Tick all options that answer to the missing proofs.

• Given

• $$\frac{OM}{QP}=\frac{MN}{PR}$$

• $$\angle N\cong\angle R$$

• SAS Similarity Theorem

• SSS Similarity Theorem

Multiple Select

Tick all options that answer to the missing proofs.

• Given

• Vertical angles are congruent

• $$\angle V\cong\angle T$$

• SAS Similarity Theorem

• AA Similarity Theorem

Multiple Select

Tick all options that answer to the missing proofs.

• $$\frac{ST}{WV}=\frac{TU}{VX}=\frac{US}{XW}$$  
  

• Vertical angles are congruent

• $$\angle V\cong\angle T$$

• $$\Delta STU\sim\Delta WVX$$  
  

• AA Similarity Theorem

Multiple Select

Tick all options that answer to the missing proofs.

• Given

• $$∠I≅∠L$$  
  

• Vertical angles are congruent

• AA Similarity Theorem

• SSS Similarity Theorem

Multiple Select

Tick all options that answer to the missing proofs.

• undefined 

• Alternate angles of a transversal are congruent
  

• Vertical angles are congruent

• $$∠MNQ≅∠ONP$$  
  

• AA Similarity Theorem

BRAVO!