How many different types of quadrilaterals can two congruent isosceles right triangles form if they share a side?

Answer 1

# The triangles are congruent, therefore triangle 1 has the same angles and lengths as triangle 2 # The triangles are isosceles, therefore two of the sides are the same length, and two of the angles are the same # The triangles are right, therefore the angle between base and height is 90 degrees Applying 2, and 3:

A triangle that is both isosceles and right has the angles 45, 90, 45 degrees and the lengths base = height = hypotenuse / sqrt(2) Applying 1:

Therefore, the triangles can share their base and heights with each other freely, but their hypotenuse can only be shared with each others hypotenuse. * If Triangle-1 shared it's hypotenuse with triangle-2's base, or height which are not the same size, the resulting shape would have five sides which is not a quadrilateral. So... # If triangle-1 shares its base with triangle-2's base, or if triangle 1 shares its height with triangle's 2 height, you are left with an equilateral triangle # If triangle-1 share its base with triangle-2's height, or if triangle 1 share its height with triangle's 2 base you are left with a trapezoid # If the triangles share a hypotenuse, you are left with a rectangle in which base = height. Otherwise known as a square There are three different types of quadrilaterals that can be made.