Question

applying properties of parallelograms
quadrilateral abcd is a parallelogram.
de = 6.1 cm and m∠dab = 120°.
what is bc?
cm
what is m∠bcd?
what is ab?
cm
what is eb?
cm

Explanation:

Step1: Use the property of parallelogram (opposite sides are equal)

In parallelogram \(ABCD\), \(BC = AD\). Given \(AD = 10\mathrm{cm}\), so \(BC=10\mathrm{cm}\)

Step2: Use the property of parallelogram (opposite angles are equal)

In parallelogram \(ABCD\), \(\angle BCD=\angle DAB\). Given \(\angle DAB = 120^{\circ}\), so \(m\angle BCD = 120^{\circ}\)

Step3: Use the property of parallelogram (opposite sides are equal)

In parallelogram \(ABCD\), \(AB = CD\). Given \(CD = 5\mathrm{cm}\), so \(AB = 5\mathrm{cm}\)

Step4: Use the property of parallelogram (diagonals bisect each other)

In parallelogram \(ABCD\), \(BE=DE\). Given \(DE = 6.1\mathrm{cm}\), so \(EB=6.1\mathrm{cm}\)

Answer:

\(BC = 10\mathrm{cm}\), \(m\angle BCD=120^{\circ}\), \(AB = 5\mathrm{cm}\), \(EB = 6.1\mathrm{cm}\)