Where a line meets a plane, where two planes meet
Construct the point where a line meets the base plane of a cube and the line where two planes of a tetrahedron meet, using the axioms of solid geometry.
- Ukraine: grade 10
- Russia: grade 10
Guide
From the Ukrainian Grade 10 textbook (algebra and calculus with geometry): §4 'Parallelism in space', item 28 'Solid figures. First facts about polyhedra', and the main type of problem in the chapter: 'construct the point where a line meets a plane' and 'construct the line where two planes meet'.
If two points of a line lie in a plane, the whole line lies in that plane (axiom A3). Two planes with a common point meet in a line through that point. So the line of intersection of two planes is fixed by two common points.
To find where a line MN meets the plane ABC, look for a line of that plane that lies in one plane with MN. If the two lines are not parallel they meet, and the meeting point belongs to MN and to the plane ABC.
In construction tasks, tap points in the picture or in the list: two taps draw a line. Then choose 'Mark a point' and tap the circle you want.