If two diagonal lines are drawn across each pair of opposite corners, they will be perpendicular to and bisect (divide into equal halves) each other at an angle of 90°. Sal proves that the diagonals of a rhombus are perpendicular, and that they intersect at the midpoints of both. Created by Sal [HOST] The two diagonals of a rhombus are perpendicular and bisect each other; Its diagonals bisect opposite angles; and. Opposite angles have equal measure. Every A rhombus is a quadrilateral with the same sides i.e. equal sides of equal length. It has 4 sides of the same length. The diagonals of a rhombus are always perpendicular to one another. A square is a quadrilateral that has 4 equal sides and each angle of 90 degrees To show why the diagonals of a rhombus are perpendicular, we can rotate the rhombus to look like a diamond and draw one diagonal as a horizontal line. Then, we can use the 1. Hint: let u,v u →, v → be the vectors originating from a vertex and drawn along the two adjacent sides, with u,u = ∥u ∥2 = ∥v ∥2 = v,v u →, u → = ‖ u → ‖ 2 = ‖ v The question is: Prove that the diagonals of a rhombus are perpendicular. This exercice is in the vector and scalar product section, so I guess the teacher is expecting it to be The diagonals of squares are equal to each other, they bisect each other, and they are perpendicular to each other. Here, we'll show this last property. Just like rectangles are a special type of parallelogram, squares are a special type of rectangles, in which all the sides are equal. Or you can think of it as a special type of rhombus
Diagonal - Math.net
In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90°). That is, each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degrees. In the figure above drag any vertex to reshape the rhombus and convince your self this is so A quadrilateral is rhombus if the opposite sides are parallel, opposite acute and obtuse angles are equal, and four equal sides. The line segment jointing the opposite vertices is known as diagonal. According to the property of rhombus, the diagonals of a rhombus are perpendicular bisector of each other The quadrilateral formed by joining the mid-points of the sides of a quadrilateral with diagonals equal is rhombus. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral with diagonals perpendicular to each other is rectangle. Hence, the correct option is (d). Suggest Corrections. 10 Prove that in a rhombus, the diagonals are perpendicular to each other. Mathematics. Question. Prove that in a rhombus, the diagonals are perpendicular to each other. But in the rectangle the diagonals don’t cut at \[{{90}^{\circ }}\]. Thus the statement given is false. If in case of square and rhombus, the diagonals are perpendicular to each other. But for rectangles, parallelograms, trapeziums the diagonals are not perpendicular. \[\therefore \] The diagonals of a rectangle are not
3.2: Other Quadrilaterals - Mathematics LibreTexts
B. If two diagonals of a rectangle are perpendicular, then the rectangle must be a square. C. If two diagonals of a rhombus are equal, then the rhombus must be a square. D. If one interior angle of a rhombus is a right angle, then the rhombus must be a square. E. If two diagonals of a parallelogram are equal, then the parallelogram must be A C and B D are diagonals, which each perpendicular to each other. P, Q, R and S are the mid-point of A B, B C, C D and A D respectively. In A B C The diagonals of a rhombus are perpendicular bisectors of one another. Given: ABCD is a rhombus. To Prove: m∠ AOD = m∠ COD = 90°. Proof: ABCD is a rhombus The rhombus is a particular case of a parallelogram. $$ e^{i \theta}= \cos {\theta}+ i \sin {\theta} = c+ i\; s = \vec{ BC} = \vec {AD}$$ Prove that the diagonals of this shape are perpendicular and equal (Quadrangle with an The diagonals of a Rhombus, however, do always intersect at right angles. 1 comment Comment on Joshua's post “No, Since the diagonals of a rhombus are perpendicular, you can use the Pythagorean theorem to find the other diagonal and then find the area 4. The diagonals of a square are perpendicular. 5. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a square. 6. If the diagonals of a quadrilateral are perpendicular, then the quadrilateral is a rhombus. 7. The diagonals of a rectangle are congruent. 8. The diagonals of a rhombus bisect the vertex angles. 9