Let X, Y and Z be the midpoints of the sides BC, CA and AB of a triangle ABC respectively. Consider the following statements: I. The quadrilateral AZXY is a parallelogram. II. The area of the quadrilateral AZXY is half of the area of the triangle ABC. Which of the statements given above is/are correct?
- A. I only
- B. II only
- C. Both I and II ✓
- D. Neither I nor II
Correct Answer: C. Both I and II
Explanation
By the midpoint theorem, XY is parallel to AB and ZX is parallel to AC. Therefore, AZXY is a parallelogram. A triangle formed by joining the midpoints divides the main triangle into four triangles of equal area. Quadrilateral AZXY consists of two such triangles, making its area exactly half of \Delta ABC.
Related questions on Geometry
- In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
- ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
- The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
- An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
- The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...