Triangles ABC and DEC are similar. Side DE is 1.8 feet, side EC is 4 feet, and side BE is 0.8 foot.
right triangle ABC with segment DE drawn so that point D is on side AC and point E is on side BC, creating right triangle DEC
Part A: Describe how to draw triangles ABC and DEC separately. Be sure to give the lengths of sides BC, DE, and EC in the description. (6 points)
Part B: Find side AB. Show each step of your work. (6 points)
Part A:
To draw triangle ABC, start by drawing a line segment of length 4 feet (side EC) as the base (BC). Then, draw a perpendicular line segment from point C to point A of length 1.8 feet (side DE). Connect points A and B to complete the triangle. The sides of triangle ABC are:
- Side BC = 4 feet
- Side AB = unknown
- Side AC = unknown
To draw triangle DEC, start by drawing a line segment of length 1.8 feet (side DE). Then, draw a perpendicular line segment from point E to point C of length 0.8 feet (side BE) and from point D to point A. Connect points D and E to complete the triangle. The sides of triangle DEC are:
- Side DE = 1.8 feet
- Side EC = 4 feet
- Side DC = unknown
Part B:
Since triangle ABC and triangle DEC are similar, their corresponding sides are proportional. This means that the ratio of corresponding sides in triangle ABC to triangle DEC is equal.
We can set up a proportion using the known sides:
AB/DE = BC/EC
Substitute the known values:
AB/1.8 = 4/4
AB/1.8 = 1
Cross multiply to solve for AB:
AB = 1.8
Therefore, the length of side AB is 1.8 feet.