REVIEW 4

Congruence, Parallelograms, and Polygons

The questions in this review section bring together the ideas from Chapters 7 and 8. They will give you a chance to see if you have mastered the idea of congruence and can solve problems about polygons. Answer all the questions, and try to express your thinking as clearly as you can.

1.   In the figure below, . Is it possible to prove ΔAOB ≅ ΔDOC? Explain.

2.   In the figure below, bisects ∠WZY and ∠WXY. Is it possible to prove ΔWZX ≅ ΔYZX? Explain.

3.   In the figure below, O is the midpoint of , and . Prove ΔAOB ≅ ΔCOD.

4.   In the figure below, bisects ∠PRQ and ∠PTR ≅ ∠QTR. Prove .

5.   In the figure below, and ∠ABC ≅ ∠DCB. Prove . Continue on to prove .

6.   Prove that in any isosceles triangle, the perpendicular bisector of the base also bisects the vertex angle.

For each property in questions 7 to 11, list the quadrilateral(s) that have that property: parallelogram, rectangle, rhombus, square, trapezoid, isosceles, trapezoid.

7.   Diagonals are congruent.

8.   Diagonals are perpendicular.

9.   Diagonals bisect one another.

10.   Diagonals bisect interior angles.

11.   Midsegment is parallel to bases.

12.   Given that M is the midpoint of and the midpoint of , prove that .

13.   Given that HOME is a parallelogram, find all possible values of x and y.

14.   If ABCD and AEFG are parallelograms, prove that∠D is supplementary to ∠F.

15.   On the space below, graph the quadrilateral with vertices P(−6, 0), Q(0, 3), R(2, −1), S (−4, −4) and prove that PQRS is a rectangle. Explain your reasoning.

16.   Each interior angle of a regular polygon measures 144°. How many sides does the polygon have?

17.   Find the number of degrees in one interior angle of a regular heptagon.

18.   Find the sum of the interior angles in a 15-sided polygon.

19.   Use compass and straightedge to inscribe a regular hexagon in the circle below.

20.   Find the area of the hexagon in question 19 if the radius of the circle is 12 cm.