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Areas of common shapes
Published in John Bird, Science and Mathematics for Engineering, 2019
The diagonals of a rhombus bisect the interior angles and opposite internal angles are equal. Thus, ∠JKM = ∠MKL = ∠JMK = ∠LMK = 30°, hence e = 30°. In triangle KLM, 30° + ∠KLM + 30° = 180° (angles in a triangle add up to 180° ), hence, ∠KLM = 120°. The diagonal JL bisects 120° ∠KLM, hence, f=120o2=60o
The Characterization Problem
Published in Stephen Hester, David Francis, Eric Livingston, Ethnographies of Reason, 2016
Stephen Hester, David Francis, Eric Livingston
Consider a rhombus. A rhombus (Figure 1) can be defined as a quadrilateral with four congruent sides. Given this definition, various properties of rhombuses can be proved—for instance, one can show that the diagonals of a rhombus are perpendicular and bisect each other. A proof of this will be given later in the chapter. For now, we’ll consider the converse proposition: if a quadrilateral has diagonals that are perpendicular and bisect each other, it must be a rhombus.
Triangles and quadrilaterals
Published in James Kidd, Ian Bell, Maths for the Building Trades, 2014
A rhombus has all the properties of a parallelogram except that its sides are of equal length. The diagonals AD and BC bisect at right angles and divide the rhombus into four congruent triangles. The area of a rhombus can be found by multiplying the base by the perpendicular height, as we did for the parallelogram.
On Vidal's trivalent explanations for defective conditional in mathematics
Published in Journal of Applied Non-Classical Logics, 2018
Yaroslav Petrukhin, Vasily Shangin
in Euclidean geometry, if a quadrilateral is a rhombus and a rectangle, then it is a square. However, the possession of only one of the properties ‘rhombus’ and ‘rectangle’ does not ensure that of the property ‘square’, as stated by (2)