Question

Which of the following types of polygons, if any, do not exist?
(i) Equilateral right triangles
(ii) Trapezoids with right angles
(iii) Kites with all acute angles

Answer 1

Kites with all acute angles.

Answer 2

(i) and (ii) only
(i) and (iii) only
(ii) and (iii) only
None of A, B, or C

Answer 3

(i) and (iii) only ---> Answer

(i) Equilateral right triangles --> An equilateral triangle is also equiangular. So, the three interior angles measure 60. A right triangle has one interior angle with measure 90. 60 does not equal 90. There is no such triangle as an equilateral right triangle.

(ii) A trapezoid can have two right angles. Possible

(iii) Kites with all acute angles --> A kite is a quadrilateral and has an interior angle sum of 360. An acute angle has measure less than 90. Four times (less than 90) is less than 360. Impossible