Revise: Similarity
Similar figures and triangles, the basic proportionality theorem, tests for similar triangles, the angle bisector theorem, the Pythagoras theorem, and special right triangles.
Similar: equal angles, proportional sides.
AB=4,BC=6,DE=6 → EF=9.
45-45-90: x,x,x√2. 30-60-90: x,x√3,2x.
30-60-90, short leg 5 → 5, 5√3, 10.
Similar: equal angles, and AB/A'B' = BC/B'C' = CA/C'A' = k.
Congruent = similar with k=1.
A line parallel to one side divides the other two proportionally: AD/DB = AE/EC.
AD=3,DB=9,AE=5 → EC=15.
AA, SAS, or SSS is enough to prove similarity.
∠A=∠D=50°, ∠B=∠E=70° → similar by AA.
a²+b²=c², proved via similar triangles from the altitude to the hypotenuse.
leg 5, hypotenuse 13 → other leg 12.
30-60-90 is half an equilateral triangle; 45-45-90 is isosceles.
45-45-90, leg 7 → hypotenuse ≈9.90.