Geo-2017-Constructions-Triangle Inequalities & Similarities
Objective
Demonstrate the Hinge Theorem by isosceles triangles.
Hinge Theorem
- Construct two isosceles triangle using the center of a circle and two points on its circumference.
- Measure the central angle
and sides
opposite them.
- Compare the lengths of the sides and create a conjecture between the lengths of the side
Hinge Theorem Conjecture
Compare the measure of the central angles and the sides of the triangles opposite them.
Similar Triangles
- Construct a triangle with a line parallel to one of the sides.
- Measure AB, AC, AD and AE.
Similar Triangle: Proportional Sides
Calculate the following ratios: How do those those ratio change or not as you drag the vertices of the triangle?
AA Proof of Similar Triangles
Any two triangles that have two congruent angles always have proportional sides. Prove that the two triangles ABC and ADE are similar by showing that they have two congruent corresponding angles.
