Presentation ~ above theme: "A dragon is a quadrilateral with exactly two bag of congruent continuous sides."— Presentation transcript:




You are watching: A quadrilateral with exactly two pairs of congruent consecutive sides

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2 A dragon is a quadrilateral with exactly two pairs of congruent continually sides.

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3 instance 1: Lucy is framing a kite with wooden dowels. She uses two dowels the measure 18 cm, one dowel that procedures 30 cm, and also two dowels that measure 27 cm. To complete the kite, she demands a dowel to place along. She has a dowel the is 36 cm long. Around how lot wood will she have actually left after cut the last dowel?

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4 example 1 continued ? ? 15cm use Pythagorean Theorem come find missing lengths 9.9cm 22.4 cm KL = 9.9+22.4=32.3 Lucy requirements to cut the dowel to be 32.3 centimeter long. The lot of timber that will stay after the cut is, 36 – 32.3  3.7 cm Lucy will have actually 3.6 centimeter of hardwood left end after the cut.

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5 dragon  cons. Sides  example 2: In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD. ∆BCD is isos. 2  political parties  isos. ∆ isos. ∆  base s  Polygon  amount Thm. CBF  CDF mBCD + mCBF + mCDF = 180° mBCD + 52° + 52° = 180°Substitute 52 because that mCBF. MBCD = 76°

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6 instance 3: Def. Of  s Polygon  sum Thm. In dragon ABCD, mDAB = 54°, and also mCDF = 52°. Uncover mABC. ADC  ABC mADC = mABC mABC + mBCD + mADC + mDAB = 360° kite  one pair opp. s  mABC + 76° + mABC + 54° = 360° Substitute. 2mABC = 230° Simplify. MABC = 115° Solve.

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7 example 4: Def. Of  s  Add. Post. Substitute. Solve. In dragon ABCD, mDAB = 54°, and mCDF = 52°. Uncover mFDA. CDA  ABC mCDA = mABC mCDF + mFDA = mABC 52° + mFDA = 115° mFDA = 63° dragon  one pair opp. s 

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8 example 5: In kite PQRS, mPQR = 78°, and also mTRS = 59°. Discover mQRT. Kite  cons. Sides  ∆PQR is isos. 2  political parties  isos. ∆ isos. ∆  base s RPQ  PRQ mPQR + mQRP + mQPR = 180° Polygon  sum Thm. 78° + mQRT + mQPT = 180° substitute 78 because that mPQR. 78° + 2mQRT = 180° Simplify. 2mQRT = 102° mQRT = 51°

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9 Assignment #48 Pg. 432 #2-6 all

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11 A trapezoid is a square with precisely one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel political parties are dubbed legs. Base angles of a trapezoid room two consecutive angles whose typical side is a base. If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the nature of one isosceles trapezoid.

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13 Isos.  trap. s base  example 1 uncover mA. Same-Side Int. s Thm. (Remember Parallel Lines) substitute 100 because that mC. Subtract 100 from both sides. Def. The  s instead of 80 because that mB mC + mB = 180° 100 + mB = 180 mB = 80° A  B mA = mB mA = 80°

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14 instance 2 KB = 21m and MF = 32 discover FB. Isos.  trap. s base  Def. The  segs. Instead of 32 for FM. Seg. Add. Post. Substitute 21 because that KB and also 32 because that KJ. Subtract 21 indigenous both sides. KJ = FM KJ = 32 KB + JB = KJ 21 + JB = 32 JB = 11 FB = 11 Diagonals that Isosceles Trapezoids are 

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15 instance 3 JN = 10, and NL = 14 discover KM. Segment add Postulate Substitute. Substitute and also simplify. Isos.  trap. s base  JL = JN + NL kilometres = JN + NL kilometres = 10 + 14 = 24

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16 example 4: advertisement = 12x – 11, and BC = 9x – 2. Find the worth of x so that ABCD is isosceles. Diags.   isosc. Trap. Def. Of  segs. Substitute 12x – 11 for advertisement and 9x – 2 for BC. Subtract 9x native both sides and include 11 come both sides. Division both sides by 3. Ad = BC 12x – 11 = 9x – 2 3x = 9 x = 3

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17 The midsegment of a trapezoid is the segment whose endpoints room the midpoints of the legs. In lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment to organize is similar to it.

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18 example 5 uncover EF. Trap. Midsegment Thm. Substitute the given values. Solve. EF = 10.75

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19 instance 6 uncover EH. Trap. Midsegment Thm. Substitute the offered values. Simplify. Multiply both sides by 2. 33 = 25 + EH Subtract 25 indigenous both sides. 13 = EH 1 16.5 = ( 25 + EH ) 2

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20 Assignment #50 Pg.

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432 #7-16 all *Assignment #49 – ar 6-6 Guided notes *Assignment #48 – Pg. 432 #2-6

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