Question

In a geometry class, the students were asked to prove the theorem below by contradiction.

Theorem: In a quadrilateral, there cannot be more than three obtuse angles.

Heather begins the proof with an assumption. Which statement will she most likely use as an assumption?


Let one angle of a quadrilateral be acute and the other three angles obtuse.

Let all angles of a quadrilateral be obtuse.

Let only one angle of a quadrilateral be obtuse.

Let one angle of a quadrilateral be obtuse and the other three angles acute.

Answer 1

b)Let all angles of quadrilateral be obtuse.
let w,x,y,z be the angles.if each angle is obtuse..i.e greater than 90
w+x+y+z=360 will not be satisfied.hence,atleast one angle in a quadrilateral must be acute.

Answer 2

thanks