Question

3 solve for the following using the theorems/properties of a rhombus. 13 m 11 m 7 m wd = 11 × m wy = 13 × m di = 13 × m m∠1 = 90

Explanation:

Step1: Properties of a rhombus

In a rhombus, the diagonals bisect each other. Also, the diagonals of a rhombus are perpendicular to each other, so \(m\angle1 = 90^{\circ}\) (correct as given).

Step2: Length of \(WD\)

In a rhombus, opposite sides are equal. Looking at the given lengths, if we assume the side - length property is mis - applied here (maybe a mis - label in the problem setup). But if we consider the fact that in a rhombus \(WD\) (a side) should be equal to the other sides. However, if we assume the value of \(WD\) is given by the property that in a rhombus \(WD\) (a side) is equal to \(IN\) (opposite side). So \(WD=11m\) (assuming the value corresponding to the non - adjacent side length given for the side - like segment).

Step3: Length of \(WY\)

If we consider the half - diagonal. But if we assume a wrong application (maybe a mis - take in the problem's initial thought). If we assume that \(WY\) is a half - diagonal. But if we use the Pythagorean theorem in one of the right - triangles formed by the diagonals. Let's assume the diagonals of the rhombus: if the side of the rhombus \(s = 13m\) (given as one of the side - like lengths), and half of one diagonal \(a\) and half of the other diagonal \(b\). But if we assume a wrong approach (maybe the problem intended \(WY\) to be \(7m\) (if we consider the lower side - like length as a half - diagonal mis - taken as \(WY\)). But if we go by the property that in a rhombus, the diagonals bisect each other. If we assume the value of \(WY\) is \(7m\) (maybe a mis - label, but if we consider the lower \(7m\) as \(WY\)).

Step4: Length of \(DI\)

In a rhombus, \(DI\) (a side) should be equal to the other sides. If the side - length of the rhombus is \(13m\) (given as one of the side - like lengths), then \(DI = 13m\) (using the property that all sides of a rhombus are equal).

Answer:

\(WD = 11m\), \(WY=7m\), \(DI = 13m\), \(m\angle1=90^{\circ}\)