6-6 Trapezoids and Kites I can use properties of kites to solve problems. I can use properties of trapezoids to solve problems. Success Criteria:  Identify properties of kites  Identify properties of trapezoids Today’s Agenda Do Now HW – Stuck Points Lesson assignment Do Now: - 4. Find FE.

6-6 Trapezoids and Kites I can use properties of kites to solve problems. I can use properties of trapezoids to solve problems. Success Criteria:  Identify properties of kites  Identify properties of trapezoids Today’s Agenda Do Now HW – Stuck Points Lesson assignment Do Now: - Solve for x x =

Properties of Kites and Trapezoids A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.

Properties of Kites and Trapezoids

Draw kite ABCD and label every angle In kite ABCD, mDAB = 54°, and mCDF = 52°.

Properties of Kites and Trapezoids Kite  cons. sides  Example 2A: Using Properties of Kites In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD. ∆BCD is isos. 2  sides  isos. ∆ isos. ∆  base s  Def. of   s Polygon  Sum Thm. CBF  CDF mCBF = mCDF mBCD + mCBF + mCDF = 180° Substitute mCDF for mCBF. Substitute 52 for mCBF. Subtract 104 from both sides. mBCD + mCBF + mCDF = 180° mBCD + 52° + 52° = 180° mBCD = 76°

Properties of Kites and Trapezoids Kite  one pair opp. s  Example 2C: Using Properties of Kites Def. of  s  Add. Post. Substitute. Solve. In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mFDA. CDA  ABC mCDA = mABC mCDF + mFDA = mABC 52° + mFDA = 115° mFDA = 63°

Properties of Kites and Trapezoids 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.

Properties of Kites and Trapezoids If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

Properties of Kites and Trapezoids The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs.

Properties of Kites and Trapezoids Isos.  trap. s base  Same-Side Int. s Thm. Def. of  s Substitute 49 for mE. mF + mE = 180° E  H mE = mH mF = 131° mF + 49° = 180° Simplify. Check It Out! Example 3a Find mF.

Properties of Kites and Trapezoids Example 5: Finding Lengths Using Midsegments Find EF. Trap. Midsegment Thm. Substitute the given values. Solve. EF = 10.75

Properties of Kites and Trapezoids Check It Out! Example 5 Find EH. Trap. Midsegment Thm. Substitute the given values. Simplify. Multiply both sides by = 25 + EH Subtract 25 from both sides. 13 = EH = ( 25 + EH ) 2

Properties of Kites and Trapezoids Assignment # 10 (13 pts) Pg 394 #7-23 odds #29 – 35 odds

Properties of Kites and Trapezoids Example 4B: Applying Conditions for Isosceles Trapezoids AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles. Diags.   isosc. trap. Def. of  segs. Substitute 12x – 11 for AD and 9x – 2 for BC. Subtract 9x from both sides and add 11 to both sides. Divide both sides by 3. AD = BC 12x – 11 = 9x – 2 3x = 9 x = 3

Properties of Kites and Trapezoids 6-6 Trapezoids and Kites I can use properties of kites to solve problems. I can use properties of trapezoids to solve problems. Success Criteria:  Identify properties of kites  Identify properties of trapezoids Today’s Agenda Do Now HW – Stuck Points Lesson assignment #12 Do Now: mWZY = 61°. Find mWXY 119°

Properties of Kites and Trapezoids Draw a kite Label vertices ABCD Draw the diagonals of a kite What do you know?!? Label the angles and sides of a kite with congruent marks

Properties of Kites and Trapezoids Draw kite PQRS and label each angle In kite PQRS, mPQR = 78°, and mTRS = 59°.

Properties of Kites and Trapezoids Check It Out! Example 2a In kite PQRS, mPQR = 78°, and mTRS = 59°. Find mQRT. Kite  cons. sides  ∆PQR is isos. 2  sides  isos. ∆ isos. ∆  base s  Def. of  s RPQ  PRQ mQPT = mQRT

Properties of Kites and Trapezoids Check It Out! Example 2a Continued Polygon  Sum Thm. Substitute 78 for mPQR. mPQR + mQRP + mQPR = 180° 78° + mQRT + mQPT = 180° Substitute. 78° + mQRT + mQRT = 180° 78° + 2mQRT = 180° 2mQRT = 102° mQRT = 51° Substitute. Subtract 78 from both sides. Divide by 2.

Properties of Kites and Trapezoids Check It Out! Example 2c Polygon  Sum Thm. Def. of  s Substitute. Simplify. In kite PQRS, mPQR = 78°, and mTRS = 59°. Find each mPSR. mSPT + mTRS + mRSP = 180° mSPT = mTRS mTRS + mTRS + mRSP = 180° 59° + 59° + mRSP = 180° mRSP = 62°

Properties of Kites and Trapezoids Check It Out! Example 3b JN = 10.6, and NL = Find KM. Def. of  segs. Segment Add Postulate Substitute. Substitute and simplify. Isos.  trap. s base  KM = JL JL = JN + NL KM = JN + NL KM = = 25.4

Properties of Kites and Trapezoids 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, mKLP = 72°, and mHJP = 49.5°. Find each measure. 2. mLHJ3. mPKL about in. 81°18°

Properties of Kites and Trapezoids Review I can use properties of quadrilaterals to solve problems. I can review for my chapter test. Success Criteria:  Identify properties of kites  Identify properties of trapezoids Today’s Agenda Do Now HW – Stuck Points Lesson HW # 14: Geopardy Do Now: 5. XV = 4.6, and WY = Find VZ. 6. Find LP.

Properties of Kites and Trapezoids Lesson Quiz: Part II Use the diagram for Items 4 and mWZY = 61°. Find mWXY. 5. XV = 4.6, and WY = Find VZ. 6. Find LP. 119°

Properties of Kites and Trapezoids Check It Out! Example 1 What if...? Daryl is going to make a kite by doubling all the measures in the kite. What is the total amount of binding needed to cover the edges of his kite? How many packages of binding must Daryl buy?

Properties of Kites and Trapezoids Check It Out! Example 1 Continued 1 Understand the Problem The answer has two parts. the total length of binding Daryl needs the number of packages of binding Daryl must buy

Properties of Kites and Trapezoids 2 Make a Plan The diagonals of a kite are perpendicular, so the four triangles are right triangles. Use the Pythagorean Theorem and the properties of kites to find the unknown side lengths. Add these lengths to find the perimeter of the kite. Check It Out! Example 1 Continued

Properties of Kites and Trapezoids Solve 3 Pyth. Thm. Check It Out! Example 1 Continued perimeter of PQRS =

Properties of Kites and Trapezoids Daryl needs approximately inches of binding. One package of binding contains 2 yards, or 72 inches. In order to have enough, Daryl must buy 3 packages of binding. Check It Out! Example 1 Continued packages of binding

Properties of Kites and Trapezoids Look Back 4 Check It Out! Example 1 Continued To estimate the perimeter, change the side lengths into decimals and round., and. The perimeter of the kite is approximately 2(54) + 2 (41) = 190. So is a reasonable answer.