SMO Open · 8. Triangles, similarity and lengths
Compute lengths and angles in triangles: right and isosceles triangles, similarity with midlines and the centroid, angle bisectors and medians, and helper constructions for angle chasing and short proofs.
Use Pythagoras, the isosceles apex altitude and special right triangles to compute lengths.
Find similar triangles from parallels, midlines and the centroid, and use the ratios correctly.
Use the angle bisector theorem, the reflection in a bisector and the median-length formula.
Choose a helper construction (equilateral triangle, midpoint) to solve angle problems.
Write a complete short proof about parallel lines with midpoints and similar triangles.