Review of Grade 10 solid geometry
Choose the right next step of a proof about skew lines, then solve problems on the angle between lines, parallel projection and a perpendicular to a plane.
- Ukraine: grade 10
- Russia: grade 10
Guide
Topic from the Ukrainian Grade 10 textbook (algebra and calculus with geometry): item 43 "Exercises to review the Grade 10 geometry course" (parallelism and perpendicularity in space). It gathers the main facts: the test for skew lines, parallel projection (it keeps parallelism and ratios of segments on one line, in particular a midpoint), the angle between lines, a line perpendicular to a plane.
Test for skew lines: if one of two lines lies in a plane and the other meets that plane at a point not on the first line, the lines are skew. A line perpendicular to a plane is perpendicular to every line of the plane; this gives right triangles in which Pythagoras' theorem works.
"Prove that" problems cannot be marked by a program, so the proof is given as a choice of the next step. The child picks a step and then explains it in their own words.