...lines are parallel, and draw through one of the middle points a line parallel to the diagonal. 46. If the diagonals of a parallelogram are equal, the figure is a rectangle. 47. If the diagonals of a parallelogram are perpendicular to each other, the figure is either a rhombus...

...parallelogram. 2. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 3. If the diagonals of a parallelogram are equal, the figure is a rectangle; if they also intersect at right angles, it is a square. 4. The straight lines joining the middle points...

...diagonal of a quadrilateral bisects two of its angles, it is perpendicular to the other diagonal. 9. If the diagonals of a parallelogram are equal, the figure is a rectangle. 10. If the diagonals of a quadrilateral bisect its angles, the figure is a rhombus. 11. Between two...

...Z s of a triangle. 5. The perimeter of a quadrilateral is greater than the sum of its diagonals. 6. If the diagonals of a parallelogram are equal, the figure is a rectangle. I. Assume construction. 2. Any two ¿ s of the ГУ may be proved to be L s ; thus, in Д s A В С...

...the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. 4. Theorem.—If the diagonals of a parallelogram are equal, the figure is a rectangle. ARRANGEMENT OF WRITTEN EXERCISES. 64. In writing out a demonstration, brevity of statement and clearness...

...if the difference of two adjacent angles is 32° ? 44. The diagonals of a rectangle are equal. 45. If the diagonals of a parallelogram are equal, the figure is a rectangle. 46. Prove by coincidence that two parallelograms are equal if they have two sides and the included...

...2HG =DC+ AB, Ax. 2 And HG=^(DC+AB). QED EXERCISES. 38. The diagonals of a rectangle are equal. 89. If the diagonals of a parallelogram are equal, the figure is a rectangle. 40. The bisectors of the interior angles of a parallelogram form a rectangle. POLYGONS. 92. A Polygon...

...one equal respectively to the base and altitude of the other, the rectangles are equal. EXERCISES. 1. If the diagonals of a parallelogram are equal, the figure is a rectangle. 2. In an oblique parallelogram the diagonals are unequal. Which is the larger? 3. The sum of all the...

...points of the sides of a triangle, is equally distant from the vertices of the triangle. EXERCISES. 48. If the diagonals of a parallelogram are equal, the figure is a rectangle. (Fig. of Prop. XLIII. & ABD and ACD are equal, and therefore /.BAD = /.ADC; also, these A are supplementary.)...

...104. If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram. Ex. 105. If the diagonals of a parallelogram are equal, the figure is a rectangle. Ex. 106. The diagonals of a rhombus are perpendicular to each other. Ex. 107. The diagonals of a square...