Why is it impossible to draw a triangle with two obtuse angles? GM2.1 Core Plenary Why is it impossible to draw a triangle with two obtuse angles? Is it possible to draw four sided shapes with these angle properties? Two acute angles, one obtuse angle and one reflex angle. Four acute angles. Two right angles, an acute angle and an obtuse angle. Two acute angles and two obtuse angles. Two reflex angles and two acute angles. Challenge How could you have predicted which of the four-sided shapes would be impossible to draw? Preamble An activity which reinforces angle properties of shapes. Allow pupils sufficient time to struggle with the first part – most might find it useful to try to draw the triangles as an aid to realise why it is impossible. Likewise with the quadrilaterals. This might be an appropriate point for pupils to be reminded/introduced to the angle sum of a quadrilateral by splitting the quadrilateral into two triangles. Possible content Using and applying knowledge of different types of angles. Resources Straight edges and plain paper. Solutions/Notes Two obtuse angles means two angles more than 90º but angles in a triangle sum to 180º. Possible, for example an arrowhead. Impossible because the sum of the angles would be less than 360º. Possible, for example a kite. Possible, for example a trapezium. Impossible because the sum of the angles would be more than 360º.