Geometry – Chapter 6 – Notes and Examples Section 6 – Properties of Kites and Trapezoids King

Properties of kites

A kite has:

 Exactly two pairs of ______sides.

 Exactly one pair of ______angles. (see diagram)

A kite has two diagonals:

 The diagonals are ______.

 Exactly one diagonal ______one pair of opposite angles. (see diagram)

 Exactly one diagonal forms two different ______triangles.

Problem 1 Problem 2 In kite ABCD, mDAB = In kite PQRS, mPQR = 78°, 54°, and mCDF = 52°. and mTRS = 59°.

Find mBCD. Find mQRT.

̅̅̅ ̅ ̅̅̅ ̅ so ∆BCD is______and ̅̅̅ ̅ ̅̅̅ ̅ so ∆PQR is______and CBF  CDF (______) mQPT = mQRT (______) mBCD + mCBF + mCDF = ______° mPQR + mQRP + mQPR = ______° mBCD + ____° + ____° = ______° 78° + mQRT + mQPT = ______° mBCD = ______° 78° + mQRT + ______= ______° Find mFDA. ____° + 2mQRT = ______°

̅̅̅ ̅ ̅̅̅ ̅ so ∆DAB is ______and 2mQRT = ______° ABF  ADF (______) mQRT = ______° mABF + mADF + mDAB = ______° Find mQPS. ______+ ______+ mDAB = ______° mQPR + mTPS = mQPS (______) mADF + mADF + ____° = ______° ____° + ____° = mQPS 2mADF + ____° = ______° ______°= mQPS mADF = ____° Find mQPT.

In kite ABCD, Problem 4 Find m∠A. AB = 8, BC = 20, m∠B = 131°, and m∠C = 38°.

Problem 3 Find AD and DC . Problem 5 Find the perimeter of kite ABCD.

A ______is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a

______. The nonparallel sides are called ______.

______of a trapezoid are two consecutive angles whose common side is a base.

If the legs of a trapezoid are congruent, the trapezoid is an ______. The following theorems state the properties of an isosceles trapezoid.

Theorem 6-6-5 is a biconditional statement. So it is true both “forward” and “backward.” Problem 6 Problem 7 Find mA. Find mF.

Problem 8 Problem 9 JN = 10.6, and NL = 14.8. Find the value of a so that Find KM. PQRS is isosceles.

Problem 10 AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.

The ______is the segment whose endpoints are the midpoints of the legs. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid

Midsegment Theorem is similar to it.

Problem 11 Problem 12 Find EF. Find EH.