Conjecture geometry is a very useful tool. A conjecture is a hypothesis. Some of the hypothesis is when 2
angles form a linear pair the addition of the angles is 180 degrees. The vertical angle conjecture is when 2
angles are vertical angles, and then both measure the same or are congruent. This way there are different
types of conjecture hypothesis like corresponding angles conjecture, alternate interior angle conjecture and
others. Conjecture geometry is useful for triangles, like SSS / ASA / SAS congruence conjectures. Even used
for quadrilateral/ pentagon/ polygon sum conjectures.
Example 1: Using SAS triangle area conjecture find the area of triangle with sides 4 cm and 8 cm
having angle between these sides C = 30 degrees.
Solution: In the given problem
Area of Triangle = (1/2 a b) sin C
Plugging in the values of a, b and C we get,
Area of Triangle = (1/2 x 4 x 8) sin 30
16 sin 30 = 16 x ½ (since sin 30 = ½)
The area of the triangle = 8 cm^2.
Example 2: Using equiangular polygon conjecture find the measure of interior angle if number of
sides of the polygon are 5.
Solution: For the given problem
Interior angle = [(n - 2) x 180] / n
plugging in the values of n we get,
Interior angle = [(5 – 2) x 180] / 3
[(3) x 180] / 3
Interior angle = 180 degrees.