6-6 properties of kites and trapezoids - nutley public … kites and... · wxyz is an isosceles...

Holt McDougal Geometry

6-6 Properties of Kites and Trapezoids

Warm Up Solve for x.

1. x2 + 38 = 3x2 – 12

2. 137 + x = 180

3.

4. Find FE.

5 or –5

43

156



• Kites and

trapezoids are

quadrilaterals

that do not fall

under the

category of

parallelograms.



A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.

Kite Properties: 1. Diagonals are perpendicular.

2. Only the pair of non-vertex

angles are congruent.

3. Diagonals only bisect the vertex angles.

4. Only the diagonal through the non-vertex angles is bisected.



Lucy is framing a kite with wooden dowels. She uses two dowels that measure 18 cm, one dowel that measures 30 cm, and two dowels that measure 27 cm. To complete the kite, she needs a dowel to place along . She has a dowel that is 36 cm long. About how much wood will she have left after cutting the last dowel?



In kite ABCD, mDAB = 54°, and mCDF = 52°. 1. Find mFDA.

2. Find mABC.

3. Find mBCD.



In kite PQRS, mPQR = 78°, and mTRS = 59°. 1. Find mQRT.

2. 2. Find mQPS.

3. Find mPSR.



• A trapezoid is a quadrilateral with exactly one pair of parallel sides.

• Each of the parallel sides is called a base. • The nonparallel sides are called legs. • Base angles of a trapezoid are two consecutive

angles whose common side is a base.



Isosceles Trapezoid

• The bases are parallel.

• The legs are congruent.

• Both pairs of base angles are congruent.

• Leg angles add up to 180 degrees.

• The diagonals are congruent.

• Diagonals do not bisect each other.



Find mA.



KB = 21.9 and MF = 32.7.

Find FB.



Find mF.



JN = 10.6, and NL = 14.8. Find KM.



Find the value of a so that PQRS is isosceles.



AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.



Find the value of x so that PQST is isosceles.



The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs.



Find EF.



Find EH.



WXYZ is an isosceles trapezoid with bases WZ and XY

and median MN.

1. Find MN if WZ = 11 and XY =

3.

2. Find m∠ XMN if m∠WZN =

78.



3. If MN = 10 and WZ = 14. Find

XY.

4. What is the value of x if

m∠MWZ = 15x – 5 and

m∠ WZN = 90 – 4x?



5. If m∠XWZ = 2x – 7 and m∠XYZ

= 117. Find x.

6. If MN= 60, XY = 4x – 1, and WZ

= 6x + 11. Find x.



7. If MN = 10x + 3, WZ = 11 and

XY = 8x + 19. Find x.

8. IF MN = 2x + 1, XY = 8 and

WZ = 3x – 3. Find x.



Lesson Quiz: Part I

1. Erin is making a kite based on the pattern below. About how much binding does Erin need to cover the edges of the kite?

In kite HJKL, mKLP = 72°, and mHJP = 49.5°. Find each measure. 2. mLHJ 3. mPKL

about 191.2 in.

81° 18°



Lesson Quiz: Part II

Use the diagram for Items 4 and 5. 4. mWZY = 61°. Find mWXY. 5. XV = 4.6, and WY = 14.2. Find VZ. 6. Find LP.

119°

9.6

18

6-6 properties of kites and trapezoids - nutley public … kites and... · wxyz is an isosceles...

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