Proportional Figures
Proportional figures maintain consistent dimension ratios when enlarged or reduced in Grade 8 math (Yoshiwara Core Math). Two figures are proportional if all corresponding dimension ratios are equal — forming a constant scale factor. A 2×3 photo and a 4×6 print are proportional (scale factor 2). Cross-multiplication verifies proportions: if a/b = c/d, then ad = bc. Proportional figures appear in scale drawings, maps, and architecture models throughout Grade 8.
Key Concepts
Property Two figures are called proportional if the ratios of corresponding distances are equal. For similar figures, the ratio of any two corresponding side lengths is equal to the scale factor.
Examples A triangle with sides 3, 5, and 7 is proportional to a triangle with sides 6, 10, and 14 because all side ratios equal 2 ($\frac{6}{3} = \frac{10}{5} = \frac{14}{7} = 2$). A 4x6 photo is enlarged to a 10x15 poster. The figures are proportional because the ratios of corresponding sides are equal: $\frac{10}{4} = 2.5$ and $\frac{15}{6} = 2.5$. A rectangle with sides 5 and 8 is not proportional to a rectangle with sides 10 and 18, because the ratios of corresponding sides are not equal ($\frac{10}{5} = 2$ but $\frac{18}{8} = 2.25$ ).
Explanation Proportional means that all corresponding parts of two figures are in the same ratio. If one side of a figure is twice as long as its corresponding side on a similar figure, then all other corresponding sides will also be twice as long.
Common Questions
What does it mean for figures to be proportional?
The ratios of all corresponding dimensions are equal, forming a consistent scale factor.
How do you check if two rectangles are proportional?
Compute side ratios. A 3×5 and 6×10: 3/6 = 5/10 = 1/2. Equal → proportional. ✓
What is cross-multiplication for in proportion problems?
Checks or solves proportions. a/b = c/d → ad = bc.
How do scale drawings use proportional figures?
If 1 cm on a map = 50 km, then 3 cm = 150 km. All measurements scale by the same ratio.
What is the difference between proportional and similar figures?
Essentially the same concept — proportional figures (scaling) and similar figures (geometry) both require equal angles and proportional sides.