What you’ll learn
Understand effects on lengths and angles.
Key idea
Positive dilation scales lengths but preserves angle measures and shape.
Lengths multiply by the positive factor, while angles remain unchanged; proposed bad measurements are not asserted as real images.
Worked example
Classify examples and non-examples for the concept 'Understand effects on lengths and angles'.
A 3-4-5-family right triangle has sides (12, 16, 20) and angle 90. Proposed factor-1/2 image sides (Fraction(6, 1), Fraction(8, 1), Fraction(10, 1)), corresponding angle 90 degrees. Classify whether BOTH length and angle measurements fit a dilation.
- Original right triangle has sides (12, 16, 20), image side ratios all 1/2: (Fraction(6, 1), Fraction(8, 1), Fraction(10, 1)).
- The corresponding right angle must remain 90 degrees, independent of the positive length scale.
Answer: Fits — all lengths scale by 1/2 and angle stays 90.
Quick Check
Classify examples and non-examples for the concept 'Understand effects on lengths and angles'.
A 3-4-5-family right triangle has sides (6, 8, 10) and angle 90. Proposed factor-1/2 image sides (Fraction(3, 1), Fraction(4, 1), Fraction(5, 1)), corresponding angle 90 degrees. Classify whether BOTH length and angle measurements fit a dilation.