2006-11-02 09:43:22 · 5 answers · asked by blaz4eva 1 in Science & Mathematics ➔ Mathematics
No. The diagonals of a parallelogram bisect each other, but they don't bisect the angles.
2006-11-02 09:53:33 · answer #1 · answered by just♪wondering 7 · 0⤊ 0⤋
The diagonal does not bisect the angles. You can show this by analyzing the two triangles that result from drawing a diagional across a parallelogram.
By symmetry, the angles in the opposite corners of the prarllelogram are equal. If the diagonal bisects the corners, then the corners of the triangles in the bisected corners must all be equal. Since two angles of the triangle are equal, the triangle must be isosceles. This means that two of the triangle's sides, hence two adjacent sides of the parallelogram must be equal, making the shape a rhombus. It follows directly then that the diagonal only bisects the angles if the shape is a rhombus. For a general parallelogram, the diagonal does not bisect the angle.
2006-11-02 11:06:40 · answer #2 · answered by Pretzels 5 · 0⤊ 0⤋
No, only in the case of the rhombus (special case square) is the diagonal a bisector. A 45° angle constructed at the vertex of a rectangle will not intersect the opposite vertex.
2006-11-02 09:54:38 · answer #3 · answered by Helmut 7 · 0⤊ 0⤋
Yes.
The diagonal of a parallelogram divides the parallelogram into 2 congruent triangles and hence the angle from which it begins into half.
2006-11-02 09:47:26 · answer #4 · answered by cmadame 3 · 0⤊ 2⤋
Yes, since by definition the sides of a parallelogram are parellel to each other, a diagonal would bisect the resulting angles.
2006-11-02 09:46:37 · answer #5 · answered by disposable_hero_too 6 · 1⤊ 3⤋