# Unit 2: Similar Triangles --- ## Similar Triangles Two triangles are **similar** if they have the same angles Note: This means that the triangles have the same shape, but might be a different size or facing a different direction --- $\Delta UVW \sim \Delta ABC$  Shrinking doesn't change the angles --- $\Delta UVW \sim \Delta ABC$  Rotating doesn't change the angles --- $\Delta UVW \sim \Delta ABC$  Shrinking, rotating or flipping doesn't change the angles --- ## Similar Triangles are Proportional $\Delta UVW \sim \Delta ABC$ this means: $\frac{UV}{AB}=\frac{UW}{AC}=\frac{VW}{BC}$ Note: This means that each side increases or decreases by a scale factor --- ## Problems 1 - 3  Find x, y, and z ---  Add additional information ---  Split into three triangles ---  Rotate the triangles ---  Flip the last triangle ---  $\Delta CDA \sim \Delta BDC \sim \Delta BCA$ ---  $\frac{x}{15}=\frac{15}{25}$ ---  $25x=15\times15=225$ --- Solve for x  $x=?$ --- Solve for y  $\frac{x}{y}=\frac{y}{25-x}$ --- Solve for z  $\frac{15}{z}=\frac{x}{y}$