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

Fill in the Blanks

Fill in the Blanks

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.

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!