Example
in the exploratory challenge, you proved the converse of a famous theorem in geometry. thales’ theorem states the following: if and are three distinct points on a circle,
and is a diameter of the circle, then ∠acb is right.
notice that, in the proof in the exploratory challenge, you started with a right angle (the corner of the colored paper) and created a circle. with thales’ theorem,
you must start with the circle and then create a right angle.
prove thales’ theorem.
a. draw circle p with distinct points and on the circle and diameter ab. prove that ∠acb is a right angle.
b. draw a third radius (pc). what types of triangles are △ and △ ? how do you know?
c. using the diagram that you just created, develop a strategy to prove thales’ theorem.
d. label the base angles of △ as ° and the base angles of △ as a°. express the measure of ∠ in terms of a° and °.
e. how can the previous conclusion be used to prove that ∠acb is a right angle?