Angle Preservation Under Dilation
Angle preservation under dilation is a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 3: Angles and Triangles. When a triangle is dilated by any scale factor k greater than 0, all three angle measures remain unchanged even though the side lengths change. This angle preservation property is the reason dilated triangles are always similar to the original.
Key Concepts
When a triangle is dilated by any scale factor $k 0$, all angle measures remain unchanged. If triangle $ABC$ is dilated to create triangle $A'B'C'$, then $\angle A = \angle A'$, $\angle B = \angle B'$, and $\angle C = \angle C'$.
Common Questions
Do angles change when a triangle is dilated?
No, dilation preserves all angle measures. When a triangle is dilated, each side length changes by the scale factor k, but every angle remains exactly the same as in the original triangle.
Why are dilated triangles similar to the original?
Because dilation preserves angles, the dilated triangle has exactly the same angle measures as the original. Since all corresponding angles are equal and sides are proportional, the triangles are similar.
What changes and what stays the same in a dilation?
Side lengths change: they are multiplied by the scale factor k. Angle measures stay the same: dilation is a similarity transformation that preserves shape but not size.
What textbook covers angle preservation under dilation in Grade 7?
Big Ideas Math Advanced 2, Chapter 3: Angles and Triangles covers angle preservation as a property of dilation transformations.