Theorem 7-2 SSS Similarity Theorem If the sides of two triangles are in proportion, then the triangles are similar.
AB
BC AC
Given:
DE
EF DF
Prove: ABC ~ ADEF
=
=
А
-
De
X
Y
B
CE
F
Plan for Proof: Take X on DE so that DX = AB. Draw a line through X
DX XYDY.
parallel to EF. Then ADEF ~ ADXY and
With the given
DE EF “DF
proportion and DX = AB, you can deduce that AC = DY and BC = XY. Thus
AABC = ADXY by SSS. Therefore, AABC ~ ADXY, and AABC ~ ADEF
by the Transitive Property of Similarity.

Atriangle has sides with lengths of 10 yards, 13 yards, and 18 yards. is it a right triangle?

How do you solve a question like this?

The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)