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Rectangles, Rhombu s e s , and Squares Pembahasan soal-soal Kelompok 3 Annisa Luthfi Fadhilah Ma’ruf ; Rosyida Khikmawati ; Rizqi Dwi Maharani ; Nadiatul Khikmah No 36 Page 287 Given : WXYZ is a square AW=BX=CY=DZ Prove : ABCD is a square Answer Statements Reasons AW BX Given <AWB <BXC Supplementary angle BW Addition of equal segment CX ∆BAW ∆CBX BA BA SAS Postulate CPCTC CB CB CD ABCD is a square DA CP Definition of square No 32 Page 286 Given : WXYZ is a rhombus R is the midpoint of WV T is the midpoint of VY S is a point of VZ Prove : ∆ RST is isosceles Answer Statements Reasons YZ <WZV <YZV Definition of rhombus WX ZV ZV ∆WZV ∆YZV RV ∆RVS SV ∆RVS SR ∆RST ∆TVS ST SAS postulate Perpendicular bisector Reflexive SV Reflexive Given TV Definition of angle bisector ∆TVS SAS postulate CPCTC Isosceles triangle No 30 Page 295 Prove that AB││DE Answer Plan : Draw AE Statements BE <BEA EA Definition of regular octagon DA Reasons <DAE AE ∆ABE ∆EDA AB ││ DE Alternate interior angle Reflexive SAS Postulate Theorem 5-2 (If two lines are cut by a transversal and a pair of alternate interior angles are congruent, then the lines are parallel) No 29 Page 295 Inscribed in a regular octagon is a star polygon. Find m<ABC. Prove that your answer is correct. Answer Plan : Draw XA and YB intersecting at T Statements Reasons XY YX Definition of regular octagon YB XA CPCTC XB AY Definition of regular octagon ∆XAB ∆YBA SSS Postulate <XAB <YBA CPCTC TB TA Side opposite congruent triangle TX TY Substraction ∆BTA and ∆XTY Are isosceles triangle <TXY <TYX ; <TBA <TAB Base angles <XTY <ATB Vertical angles <TXY <TAB Substraction ………Answer Statements Reasons m<XBA + m<BXY = 180 <XBA is suplementary to <BXY m<BXY=135 Theorem 8-15 (The measure of an angle of a regular pentagon of n sides is (n-2)/n x 180) m<XBA = m<EBC = 45 Same as above pattern m<ABC = 45 m<ABC = 135-2(45) =45 No 16 Page 291 Given : ∆ABC is isosceles with AB AC, <AED <B Prove : BCDE is a trapezoid with BE CD Answer Statements <AED <B ED ││ BC BCDE is a trapezoid Reasons Given Theorem 5-1 (if two lines are cut by a transversal and a pair of corresponding angles are congruent, then the line are parallel) Definition of trapezoid (Trapezoid is a quadrilateral with exactly one of parallel side) No 9 Page 298 The figures shown are two overlapping rectangles. Find the sum, a+b+c+d. Answer Based on the figures shown that a,b,c,d is the exterior angles of a poygon that built from two overlapping rectangles. So, the sum a+b+c+d=360 (theorem 8-16) (The sum of the measures of the exterior angles of an polygon, one each vertex, is 360)
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