mSPT + mTRS + mRSP = 180° mSPT = mTRS Def. mQPS = 110°Ĭheck It Out! Example 2c In kite PQRS, mPQR = 78°, and mTRS = 59°. ![]() mQPS = mQRT + mTRS mQPS = mQRT + 59° Substitute. 2mQRT = 102° mQRT = 51° Divide by 2.Ĭheck It Out! Example 2b In kite PQRS, mPQR = 78°, and mTRS = 59°. of sĬheck It Out! Example 2a Continued mPQR + mQRP + mQPR = 180° Polygon Sum Thm. mFDA = 63° Solve.Ĭheck It Out! Example 2a In kite PQRS, mPQR = 78°, and mTRS = 59°. mABC = 115° Solve.Įxample 2C: Using Properties of Kites In kite ABCD, mDAB = 54°, and mCDF = 52°. mABC + mBCD + mADC + mDAB = 360° Substitute mABC for mADC. mBCD = 76°Įxample 2B: Using Properties of Kites In kite ABCD, mDAB = 54°, and mCDF = 52°. mBCD + mCDF+ mCDF = 180° Substitute 52 for mCDF. mBCD + mCBF + mCDF = 180°Įxample 2A Continued mBCD + mCBF + mCDF = 180° Substitute mCDF for mCBF. ∆base s CBF CDF mCBF = mCDF Def. 4 Check It Out! Example 1 Continued Look BackĮxample 2A: Using Properties of Kites In kite ABCD, mDAB = 54°, and mCDF = 52°. The perimeter of the kite is approximately 2(54) + 2 (41) = 190. To estimate the perimeter, change the side lengths into decimals and round. In order to have enough, Daryl must buy 3 packages of binding. One package of binding contains 2 yards, or 72 inches. Packages of binding Check It Out! Example 1 Continued Daryl needs approximately 191.3 inches of binding. ![]() Add these lengths to find the perimeter of the kite.ģ Solve perimeter of PQRS = Check It Out! Example 1 Continued Pyth. Use the Pythagorean Theorem and the properties of kites to find the unknown side lengths. Make a Plan 2 Check It Out! Example 1 Continued The diagonals of a kite are perpendicular, so the four triangles are right triangles. the number of packages of binding Daryl must buy.the total length of binding Daryl needs.What is the total amount of binding needed to cover the edges of his kite? How many packages of binding must Daryl buy?ġ Understand the Problem Check It Out! Example 1 Continued ![]() 4 Example 1 Continued Look BackĬheck It Out! Example 1 What if.?Daryl is going to make a kite by doubling all the measures in the kite. So the wood remaining is approximately 36 – 32 = 4. The length of the diagonal is approximately 10 + 22 = 32. To estimate the length of the diagonal, change the side length into decimals and round. The amount of wood that will remain after the cut is, 36 – 32.4 3.6 cm Lucy will have 3.6 cm of wood left over after the cut. Pythagorean Thm.Įxample 1 Continued Lucy needs to cut the dowel to be 32.4 cm long. 2 Example 1 Continued The answer will be the amount of wood Lucy has left after cutting the dowel.ģ Solve Example 1 Continued N bisects JM. Use the Pythagorean Theorem and the properties of kites to find, and. Let N represent the intersection of the diagonals. About how much wood will she have left after cutting the last dowel?ġ Make a Plan Understand the Problem The diagonals of a kite are perpendicular, so the four triangles are right triangles. To complete the kite, she needs a dowel to place along. She uses two dowels that measure 18 cm, one dowel that measures 30 cm, and two dowels that measure 27 cm. Vocabulary kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid isosceles trapezoid midsegment of a trapezoidĪ kiteis a quadrilateral with exactly two pairs of congruent consecutive sides.Įxample 1: Problem-Solving Application Lucy is framing a kite with wooden dowels. Use properties of trapezoids to solve problems. ![]() Objectives Use properties of kites to solve problems.
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