Unit Squares and Triangles
- Bill Lombard
Unit Squares and Triangles A nice problem that involves four geometric transformations. Given: Three unit squares and two line segments connecting two pairs of vertices. What is the area of △ELF? Two solutions are given on the website below; this solution uses transformations, a CCSS feature. Since △ELF ~ △HIF ≅ △EFA, and the length of side FH = √5, then the area of △HIF = 5(△ELF) since area grows by the square of the scale factor. Hence the area of △ELF = 0.2 units. There are four steps to the transformation: 1- reflect △ELF about line EF 2- rotate △ELF about point F 3- dilate △ELF about point F by factor of √5 4- translate △ELF 2 units down - from https://www.illustrativemathematics.org/illustrations/918
1- Why are the three triangles similar? 2- Can you find the area of triangle ELF another way?