Ch 5 Worksheet Key

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Ch 5 Worksheet L1 Key Name ___________________________ 5.3 Page 271 Proof of Isosceles Trapezoid Diagonals Conjecture Conjecture: The diagonals of an isosceles trapezoid are congruent. Given: Isosceles trapezoid TRAP with TP = RA. Show: Diagonals are congruent, TA = RP. TR = TR PT Given = RA Same Segment. Isosceles trapezoid TRAP Given m∠ PTR= m∠TRA Isosceles Trap. base angles = ΔPTR ≅ ΔART SAS Cong. Conj. TA = RP CPCTC 5.3 Page 274 Exercise #19 5.4 Page 279 Exercise #14 a = 80, b = 20, c = 160, d = 20, e = 80, f = 80, g = 110, h = 70, m = 110, n = 100 a = 54, b = 72, c = 108, d = 72, e = 162, f = 18, g = 81, h = 49.5, i = 130.5, k = 49.5, m = 162, n = 99 S. Stirling Page 4 of 8
Ch 5 Worksheet L1 Key Name ___________________________ Proof of the Parallelogram Opposite Angles Conjecture Conjecture: The opposite angles of a parallelogram are congruent. R 2 Given: Parallelogram PARL with diagonal AL . Prove: ∠PAR ≅∠PLR and ∠R≅∠ P. 1 L Parallelogram PARL Given LP AR Def. of Parallelogram PA LR Def. of Parallelogram m∠ 1= m∠ 4 If ||, AIA cong. m∠ R= m∠ P m∠ 2= m∠ 3 If ||, AIA cong. m∠ 2+ m∠ 1= m∠ 3+ m∠ 4 A Addition m∠ PLR= m∠ PAR 4 3 P If 2 angles of one triangle = 2 angles of another, the 3 rd angles are =. Substitution Proof of the Parallelogram Opposite Sides Conjecture Conjecture: The opposite sides of a parallelogram are congruent. P A Given: Parallelogram PARL with diagonal PR . Prove: PL ≅ RA and PA ≅ LR . Parallelogram PARL Given PA LR Def. of Parallelogram ∠APR ≅∠LRP If ||, AIA cong. L R ∠L ≅∠ A Opposite angles of Parallelogram = ΔPAR ≅ΔRLP AAS Cong. Conj. PR = PR PL ≅ RA and PA ≅ LR Same Segment. CPCTC S. Stirling Page 5 of 8
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