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, mDAB = In kite PQRS, mPQR = 78°, 54°, and mCDF = 52°. and mTRS = 59°. Find mBCD. Find mQRT. ̅̅̅ ̅ ̅̅̅ ̅ so ∆BCD is______________ and ̅̅̅ ̅ ̅̅̅ ̅ so ∆PQR is______________ and CBF CDF (__________________ ) mQPT = mQRT (__________________ ) mBCD + mCBF + mCDF = _______° mPQR + mQRP + mQPR = _______° mBCD + ____° + ____° = _______° 78° + mQRT + mQPT = _______° mBCD = _______° 78° + mQRT + _______= _______° Find mFDA. ____° + 2mQRT = _______° ̅̅̅ ̅ ̅̅̅ ̅ so ∆DAB is ______________ and 2mQRT = _______° ABF ADF (__________________ ) mQRT = _______° mABF + mADF + mDAB = _______° Find mQPS. _________ + _________ + mDAB = _______° mQPR + mTPS = mQPS (______________ ) mADF + mADF + ____° = _______° ____° + ____° = mQPS 2mADF + ____° = _______° _______°= mQPS mADF = ____° Find mQPT. 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 mA. Find mF. 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. .