Question

6.
describe the figure using as many of these words as possible: rectangle, trapezoid, square, quadrilateral, parallelogram, rhombus.
figure
a trapezoid, quadrilateral
b
c rhombus, quadrilateral
d quadrilateral, parallelogram
e square, parallelogram
7.
abcd is a parallelogram. if m∠dab = 115, then m∠bcd = ______ . (the diagram is not to scale.)
figure
a 75
b
c 125
d 115
e 65

Explanation:

Question 6

A quadrilateral is a four - sided figure. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. The figure has two pairs of opposite sides parallel (indicated by the arrows), so it is a parallelogram and also a quadrilateral. A trapezoid has only one pair of parallel sides, so it's not a trapezoid. A rhombus has all sides equal, and there's no indication of that here. A square has all sides equal and all angles 90 degrees, which is not indicated. So the correct description is quadrilateral, parallelogram.

Step1: Recall the property of parallelograms

In a parallelogram, opposite angles are equal. In parallelogram \(ABCD\), \(\angle DAB\) and \(\angle BCD\) are opposite angles.

Step2: Apply the property

Since \(\angle DAB\) and \(\angle BCD\) are opposite angles of parallelogram \(ABCD\), \(m\angle BCD=m\angle DAB\).
We know that \(m\angle DAB = 115^{\circ}\), so \(m\angle BCD=115^{\circ}\).

Answer:

D. quadrilateral, parallelogram

Question 7