Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Proofs about triangles
Prove triangle-angle base-angle midsegment and median relationships
Problem types
- Perpendicular bisector and midsegment properties
- Use a triangle theorem in a proof
- Prove triangle and perpendicular-bisector theorems
Builds on
- Congruence criteria for triangles
- Writing and critiquing a geometric proof
- Proofs about lines and angles · Earlier idea
Equal alternate interior angles from a line parallel to one side are the key step in the proof that a triangle's angles total 180 degrees.
Leads to
- Proofs that use coordinates · See it applied
The midsegment and median facts can be checked with coordinates: a midsegment has half the vector of the side it is parallel to.
- Deriving the laws of sines and cosines · See it applied
The altitude and congruence reasoning in triangle proofs is used to derive the laws of sines and cosines.
Related skills
- Vectors and their components · Related idea
A midsegment of a triangle is half the vector of the side it is parallel to.
- Proofs about parallelograms · Shared foundations
- Theorems about circles · Shared foundations
- Why the circle and solid formulas hold · Shared foundations
- Proving triangles similar · Shared foundations
Open the interactive map to explore lessons and skill connections.