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Ch8:Quadrilaterals

PRACTICE PROBLEMS

Prerequisite Skills: 1.Identifying angle pairs2. Using the Triangle Sum Theorem3.Using parallel lines

Learning Targets:

• Classify polygons
• Find angle measures in polygons
• Use properties of tessellations
• Find angle and side measures in parallelograms
• Use properties to identify parallelograms
• Use properties of rhombuses, rectangles, squares
• Use properties of trapezoids and kites

Syllabus: Ch8 Quadrilaterals

***Syllabus subject to change due to weather, pep rallies, illness, etc

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1.6 and8.1 Angles of a Polygon Practice Problems

3. Name the polygon that has the following condition.

a) Interior angle = 108°

b) Exterior angle = 40°

c) Interior angle = 120°

d) Exterior angle = 30°

4. The home plate in baseball which is a pentagon that has three right angles. The other two angles are equal. Find the measure of each of the missing angles.

5. In the drawing, a regular polygon is partially covered by a trapezoid. How many sides does the covered polygon have?

6. One piece of the birdhouse that Natalie is building is shaped like a regular pentagon, as shown in the picture. If side AE is extended to point F, what is the measure of the exterior angle DEF?

Find the value of x.

7.

8.

Find the measures of an interior angle and an exterior angle of the indicated polygon.

9.Regular triangle

10.Regular 16-gon

11.Regular 45-gon

8.2 Properties of Parallelograms and 8.3 Proving Parallelograms Practice Problems

Find the measure of the indicated angle in the parallelogram.

1.) Find mB2.) Find mM

Find the value of each variable in the parallelogram.

3.)4.)

5.) Find the value of each variable in the parallelogram.

6.) In parallelogram WXYZ, mW is 50 degrees more than mX. Sketch parallelogram WXYZ. Find the measure of each interior angle. Then label each angle with its measure.

Find the indicated measure in parallelogram ABCD.

7.) mAEB8.) mBAE

9.) mAED10.) mECB

11.) mBAD12.) mDCE

13.) mADC14.) mDCB

15.) Use the diagram of parallelogram MNOP at the right to copy and complete the statement.

a) b)

c) d)

e) f)

g) h)

What theorem can you use to show that the quadrilateral is a parallelogram?

16.) 17.)18.) 19.)

For what value of x is the quadrilateral a parallelogram?

20.) 21.)

22.) The vertices of quadrilateral ABCD are given. Draw ABCD in a coordinate plane and show that it is a parallelogram.

Review 8.1-8.3

Find the sum of the measures of the interior angles of the convex polygon.

1. nonagon2. 18gon

Find the value of x.

3.4.5.

6. Name the polygon that has the following condition.

a) Interior angle = 162°

b) Exterior angle = 72°

c) Interior angle = 120°

d) Exterior angle = 45°

Find the sum of the measure of the exterior angles of the convex polygon.

7. nonagon8. 15gon

Find the value of x.

9.10.

Complete each statement. Quadrilateral RSTW is a parallelogram.

11. // _____

12. XT  _____

13. WTS  _____

14. ΔRWT Δ _____

True or False.

______15. Every parallelogram is a quadrilateral.

______16. There exists a parallelogram FISH such that mH = 65° and mS = 115°.

______17. is a diagonal of parallelogram QUAD.
______18. The consecutive angles of a parallelogram are congruent.

In # 19 – 26, quadrilateral CDEF is a parallelogram. Answer the following questions.

______19. CE = 18, CX = ?

______20. FX = 12, FD = ?

______21. mCDE = 72°, mEFC = ?

______22. m2 = 74°, m3 = ?

______23. mCFE = 14x – 11, mEDC = 12x +3, x = ?

______24. m3 = 2x + 6, m4 = 3x, mFED = 106°, x = ?

______25. FX = 5y – 4, FD = 32, y = ?

______26. CE = 6y – 2, XE = 14, y = ?

Tessellations

1. Explain how you can tell whether a regular polygon can tessellate a plane.

8.4 Properties of Rhombuses, Rectangles and Squares

8.5 Trapezoids Practice Problems

Classify the parallelogram. Explain your reasoning.

1.) 2.) 3.)

4.) 5.) 6.)

Name each quadrilateral – parallelogram, rectangle, rhombus, and square – for which the statement is true.

7.) It is equilateral.8.) The diagonals are congruent.

9.) It can contain obtuse angles.10.) It contains no acute angles.

Decide whether the statement is true or false. Explain why.

11.) If a quadrilateral is a rectangle, then it is a parallelogram.

12.) If a quadrilateral is a parallelogram, then it is a rhombus.

13.) If a quadrilateral is a square, then it is a rhombus.

14.) If a quadrilateral is a rectangle, then it is a rhombus.

15.) If a rhombus is a square, then it is a rectangle.

Classify the special quadrilateral. Then find the values of x and y.

16.) 17.)

The diagonals of rhombus PQRS intersect at T. Given that mRPS = 30° and RT = 6, find the indicated measure.

18.) mQPR19.) mQTP

20.) RP21.) QT

The diagonals of rectangle WXYZ intersect at P. Given that mYXZ = 50° and XZ = 12, find the indicated measure.

22.) mWXZ23.) mWPX

24.) PY25.) WX

The diagonals of square DEFG intersect at H. Given that EH = 5, find the indicated measure.

26.) mGHF27.) mDGH

28.) HF29.) DE

Tell whether the statement is always, sometimes, or never true.

30.) A trapezoid is a parallelogram.

31.) The bases of a trapezoid are parallel.

32.) The base angles of an isosceles trapezoid are congruent.

33.) The legs of a trapezoid are congruent.

Points J, K, L, and M are vertices of a quadrilateral. Determine whether JKLM is a trapezoid.

34.) J(-1, 1), K(0, 3), L(3, 3), M(4, -1)

1

Find mF, mG, and mH.

35.)

Find the length of the midsegment of the trapezoid.

36.)

1

Find the value of x.

37.) 38.)

Ch 8 Test Review

**Make sure you know the different properties of each type of quadrilateral**

1.) The of a trapezoid is parallel to the bases.

2.) A(n) of a polygon is a segment whose endpoints are nonconsecutive vertices.

3.) Describe the different ways you can show that a trapezoid is an isosceles trapezoid.

4.) The sum of the measures of the interior angles of a convex regular polygon is 1080°. Classify the polygon by the number of sides. What is the measure of each interior angle?

5.) The sum of the measures of the interior angles of a convex regular polygon is 3960°. Classify the polygon by the number of sides. What is the measure of each interior angle?

Find the value of x.

6.) 7.) 8.)

9.) In a regular nonagon, the exterior angles are all congruent. What is the measure of one of the exterior angles? Explain.

10.) Quadrilateral WXYZ is a parallelogram. Find the values of x and y.

Find the value of each variable in the parallelogram.

11.) 12.)

13.) In parallelogram PQRS, PQ = 5 centimeters, QR = 10 centimeters, and mPQR = 36°. Sketch PQRS. Find and label all of its side lengths and interior angle measures.

14.) The perimeter of parallelogram EFGH is 16 inches. If EF is 5 inches, find the lengths of all the other sides of EFGH. Explain your reasoning.

For what value of x is the quadrilateral a parallelogram?

15.) 16.)

Classify the special quadrilateral. Then find the values of x and y.

17.) 18.)

19.) Quadrilateral DEFG is a trapezoid. Find mG and mE.

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