Geometry Test 2

1. Prove that the sum of the squares of the sides of a rectangle is equal to the sum of the squares of its diagonals. 2. Adjacent sides of a parallelogram are 11 cm and 17 cm. Its one diagonal is 26 cm. Find its other diagonal. 3. The walls of the buildings on opposite sides of a street are parallel to each other. A ladder 20 m long is placed so that its top just reaches the window of one building at the height 16 m. On turning the ladder over to the other side of the street, its top touches other building at the height 12m. Find the width of the street. 4. In a right angled triangle, hypotenuse is 61 cm and one side is 11 cm. Find its other side and area of the triangle. 5. Find the side of the square, whose diagonal is 16 cm. 6. In a right angled triangle, sides making right angle are 24 cm and 18 cm. Find its hypotenuse. 7. Find the diagonal of a square whose side is 20 cm. 8. Side of a rhombus is 10 cm, and one of its diagonals is 16 cm. Find the length of other diagonal. 9. If the areas of two similar triangles are equal, then prove that they are congruent.