Chapter 7 - Exercises

The rhombus represented in Figure 1 was constructed by connecting the centers of the four tangent circles. All these circles have the same radii measure. Doubling the radius of two of the circumferences, which are centered on opposite vertices of the rhombus, and keeping the original configuration of the tangencies. When taking these steps a situation arises as illustrated by Figure 2. The perimeter of the rhombus in Figure 2, when compared to the perimeter of the rhombus in Figure 1, increases by:

2-If ABCD is a trapezoid of bases AB and CD, determine x and y.

3-The median of a trapezoid measures 60 cm and the smallest base is  the largest base. Determine the measurements of the bases.

4 (Dolce & Pompeu) In the following items, mark the correct alternatives:

5 (Dolce & Pompeu) - The sum of two opposite angles of a parallelogram is equal to the sum of the other two opposite angles. Determine these angles.

6 (Dolce & Pompeu) - In a rectangular trapezoid, the angle bisector of a right angle connects with the bisector of the acute angle of the trapezoid. This forms an angle of 110º. Determine the largest angle of the trapezoid.

7- If the polygon ABCD is a square and the polygon BCE is an equilateral triangle, then x measures:

8 (Dolce & Pompeu) - The triangle ABC has sides AN = 9, BC = 14 and AC = 11. In this triangle the points D, E and F are midpoints of AB, AC and BC, respectively. Calculate the perimeter of the triangle DEF.