Find the smaller side of a rectangular trapezoid, the bases of which are 10 cm and 6 cm

Find the smaller side of a rectangular trapezoid, the bases of which are 10 cm and 6 cm and one of the corners is 45 degrees.

1. A, B, C, D – the tops of the trapezoid. BC = 6 cm. AD = 10 cm. ∠D = 45 °. ∠А = ∠В = 90 °. CE is the height drawn to AD.

2. Calculate the degree measure ∠DCE:

∠DCE = 180 – ∠CED – ∠D = 180 – 90 – 45 = 45 °.

3. The angles on the CD side of the CDE triangle are equal, therefore, its sides CE and DE are also equal.

4. BE = AE = 6 cm. DE = AD – AE = 10 – 6 = 4 cm.

5.CE = DE = AB = 4 cm.

6. In a rectangular trapezoid, according to its properties, the height is equal to the smaller lateral side.

AB = 4 cm – smaller lateral side.