Geometry

Name: __________________ Date: ______________

Polygons & Quadrilaterals Chapter 6 ReviewSlope: Midpoint Formula:

Distance Formula: Polygon Interior Angle Formula:

Parallel Lines: Perpendicular Lines:

Conditions for Parallelograms: Conditions for Rectangles:

Conditions for Rhombi: Conditions for Squares:

Conditions for Trapezoids: Conditions for Kites:

1. Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.

2. Find the sum of the interior angle measures of a convex 16-gon.

3. The surface of a trampoline is in the shape of a regular hexagon. Find the measure of each interior angle of the trampoline.

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Geometry

4. Find the measure of each exterior angle of a regular decagon.

5. A pantograph is used to copy drawings. Its legs form a parallelogram. In parallelogram JKLM, LM = 17 cm, KN= 13.5 cm, and m∠KJM = 102°. Find each measure.KM KJ MN m∠JKL m∠JML m∠KLM

6. WXYZ is a parallelogram. Find each measure.WX YZm∠X m∠W

7. Show (prove) that the quadrilateral with the given vertices is a parallelogram.W (-5, -2) , X (-3, 3) , Y (3, 5) , Z (1, 0)

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Geometry

What is the perimeter of the quadrilateral?

8. Show (prove) that the quadrilateral with the given vertices is a parallelogram.R (-1, -5) , S (-2, -1) , T (4, -1) , U (5, -5)

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Geometry

What is the perimeter of the quadrilateral?

9. Show that GHJK is a parallelogram for m = 12 and n = 9.5.

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Geometry

10. Show that RSTV is a parallelogram for x = 6 and y = 4.5.

11. The flag of Jamaica is a rectangle with stripes along the diagonals. In rectangle QRST, QS= 80.5, and RS= 36. Find each length.

SP

QT

TR

TP

12. GHJK is a rhombus. Find the measure of HJ, m∠HJG and m∠GHJ if m∠JLH = (4b - 6)°and m∠JKH = (2b + 11)°

13. Determine if the conclusion is valid. If not, tell what additional information is needed to make it valid.Given: AC ⊥ BD Conclusion: ABCD is a rhombus.

14. The vertices of square JKLM are J (-3, -5) , K (-4, 1) , L (2, 2) , and M (3, -4) . Show that the diagonals of square JKLM are congruent perpendicular bisectors of each other. (distance, slope, midpoint)

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Geometry

15. Tell whether each statement is sometimes, always, or never true. A rectangle is a parallelogram. A rhombus is a square.

A parallelogram is a rhombus. A rhombus is a rectangle.

A square is a rhombus. A rectangle is a quadrilateral.

A square is a rectangle. A rectangle is a square.

16. In kite EFGH, m∠FHG= 68°, and m∠FEH= 62°. Find each measure.

m∠FEJ m∠EHJ

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Geometry

m∠FGJ m∠EHG

17. Find m∠R.

18. Use the diagonals to determine (prove) whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply.P (-5, 2) , Q (4, 5) , R (6, -1) , S (-3, -4) Is it a rectangle?

Is it a rhombus?

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Geometry

Is it a square?

19. YZ = 34.2, and VX = 53.4. Find WZ.

20. A dulcimer is a trapezoid-shaped stringed instrument. The bases are 43 in. and 23 in. long. If a string is attached at the midpoint of each leg of the trapezoid, how long is the string?

21. Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

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Geometry

22. Find the measure of each interior angle of hexagon ABCDEF.

23. Find the measure of each exterior angle in polygon RSTUV.

24. Tell whether each quadrilateral is a parallelogram, rectangle, rhombus, or square. Give all the names that apply

25. In kite EFGH, m∠FEJ= 25°, and m∠FGJ= 57°. Find each measure.

m∠GFJ

m∠JFE

m∠GHE

26. In kite PQRS, m∠PQR= 78°, and m∠TRS= 59°. Find each measure.

m∠QRT

m∠QPS

m∠PSR

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Geometry

27. Figure XYWZ is an isosceles trapezoid. Find the remaining three angle measures.

28. RT= 24.1, and QP= 9.6. Find PS.

29. Find the value of y so that EFGH is isosceles.

30. JL= 5z+ 3, and KM = 9z- 12. Find the value of zso that JKLM is isosceles.

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Geometry

31. Use the definition of a parallelogram to show that the quadrilateral with vertices K(–3, 0), L(–5, 7), M(3, 5), and N(5, –2) is a parallelogram.

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