Kai Salinas finishes Geometry on Khan Academy

Plowing through Khan Academy, Kai Salinas finished high school geometry before turning 10 years old! Honestly, the boy continues to amaze us. He refuses to write things down, i.e. intermediary results. He doesn’t read too carefully… yet he somehow just gets it. I didn’t help him at all with high school geometry. I peppered him with ideas about proof by contradiction and proof by construction, but as far as the actual problem sets, he reasoned through each of them himself!

Geometry Overview

Congruence

• Experiment with transformations in the plane
• Understand congruence in terms of rigid motions
• Prove geometric theorems
• Make geometric constructions

Similarity, Right Triangles, and Trigonometry

• Understand similarity in terms of similarity transformations
• Prove theorems involving similarity
• Define trigonometric ratios and solve problems involving right triangles
• Apply trigonometry to general triangles

Circles

• Understand and apply theorems about circles
• Find arc lengths and areas of sectors of circles

Expressing Geometric Properties with Equations

• Translate between the geometric description and the equation for a conic section
• Use coordinates to prove simple geometric theorems algebraically

Geometric Measurement and Dimension

• Explain volume formulas and use them to solve problems
• Visualize relationships between two-dimensional and three-dimensional objects

Modeling with Geometry

• Apply geometric concepts in modeling situations

Kai has achieved Abacus Level 1 at 9 years old. Next year, he will test at Mental Level 1. It’s difficult for me to wrap my head around preparing all year for an abacus competition that only occurs once a year. If you wanted you, you could find a golf tournament or chess tournament any weekend of the year. For abacus however, you must wait for the annual competition held each May.

This Fall, Kai has decided to help teach other kids in abacus Also, he is now preparing for his first AMC 8 competition.