Similar figures. Figures with same shape. They are not necessarily the same size.
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:
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)
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.
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
EF = QR
EG = QS
FG = RS
Triangles EFG and QRS are similar. Create a proportion matching the corresponding sides.
Trapezoid ABCD is similar to Trapezoid MNOP. Determine the value of x.
The two figures are similar. Find the missing values
Similar trapezoids are shown. What is the value of X?
Similar Triangles 1
Similar Triangles 2
Similar Triangles 3
Find the Missing Side of Similar Triangles 1
Similar Shapes
Similar Rectangles
Scale Factor and Area
SF01 Scale_Drawing
SF02 Scale_Factor
SF03 Similar Figures (Indirect Measurement)
SF05 Similar Figures_Missing Side
SF06 Scale_Perimeter
SF10 Similar_Rectangles_1
SF11 Similar_Rectangles_2
SF12 Similar_Rectangles_3
SF13 Similar_Triangles 1
SF14 Similar Triangles 2
SF15 Similar_Cylinders
Vocabulary:
Congruent shapes have all corresponding sides and corresponding angles exactly equal (symbol: ≅)
Similar shapes have the same shape, but not necessarily the same size [corresponding angles are exactly equal] (symbol: ≈ or ~ )