|Triangles Lesson Plan:
- Students will be able to state, proof, and use the theorem that
states that the sum of any two lengths of any triangle is greater than
the length of the third side.
Expected prior knowledge:
- Basic triangle properties
- Theorem that states two sides of a triangle are equal if and only if
their opposite angles are equal
- Theorem that states if two angles of a triangle are unequal, then
the sides opposite are unequal in the same order
- Law of cosines
- Give each of the students a set of three segments (that cannot be
formed into a triangle; i.e., the sum of two of the sides is not greater
than the third side) and ask them to form a triangle using their the 3
segments they were given.
- Students see that not every set of three segments can form a
- Gives students motivation to figure out what must be true about
three segments to form a triangle.
- Give students each a “hinge” (see below) with two fixed lengths of
triangle sides and a ruler to form the third side.
- Discuss the findings and the conjecture
- Walk through as a class the outline of a formal proof to show our
conjecture is always true and not just for the examples we tried in
- Optional: Show students another way to prove the same theorem. As a
class, go through how you could use the law of
cosines in a proof.
- Make up a worksheet for homework with further problems relating to