Similar Figures

Similar figures. Figures with same shape. They are not necessarily the same size.

similar5
Two polygons are similar if their corresponding angles are congruent and the measures of their corresponding sides are in proportion  (scale factor).

“~” is the sign for “is similar to”.

Polygons can still be similar even if one of them is rotated, example:

Rotated

Essential Question:
If a polygon is enlarged or reduced, which parts changes and which parts remains the same?

Vocabulary:

  • Similar
  • Congruent
  • Enlarged
  • Reduced
  • Scale factor

 

Examples:

Triangles EFG and QRS are similar. The length of the sides of EFG are 3, 4, and 5. The length of the smallest side of QRS is 7.5, what is the length of the longest side of QRS?

(All units in the examples are in centimeters)

EFG



Triangles EFG and QRS are similar. The length of the sides of EFG are 3, 4, and 5. The length of the smallest side of QRS is 7.5, what is the scale factor?

Two triangles are similar if one of them is larger than the other by a Scale Factor.

ScaleFactor

Triangles EFG and QRS are similar. The length of the sides of EFG are 3, 4, and 5. The length of the smallest side of QRS is 7.5, what is the perimeter of QRS?

Perimeter of triangle EFG = 3+4+5 = 12

A scale factor is simply a number that multiplies the dimensions of a shape.

Perimeter of triangle QRS = 2.5 (3+4+5) = (7.5 + 10 + 12.5) = 30

Triangles EFG and QRS are similar. Find the corresponding sides

Triangles

 

 

EF = QR

EG = QS

FG = RS

Triangles EFG and QRS are similar. Create a proportion matching the corresponding sides.

ratios

 

proporciones

 

Trapezoid ABCD is similar to Trapezoid MNOP. Determine the value of x.

Trapezoids

 

solpro

The two figures are similar. Find the missing values

 

Similar trapezoids are shown. What is the value of X?