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Kelompok 3Annisa Luthfi Fadhilah Ma’ruf ; Rosyida Khikmawati ; Rizqi Dwi Maharani ; Nadiatul Khikmah
Rectangles, Rhombuses, and
Squares
Pembahasan soal-soal
Given : WXYZ is a squareAW=BX=CY=DZ
Prove : ABCD is a square
No 36 Page 287
AnswerStatements Reasons
AW BX Given
<AWB <BXC Supplementary angle
BW CX Addition of equal segment
∆BAW ∆CBX SAS Postulate
BA CB CPCTC
BA CB CD DA CP
ABCD is a square Definition of square
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
No 32 Page 286
AnswerStatements Reasons
WX YZ Definition of rhombus
<WZV <YZV Definition of angle bisector
ZV ZV Reflexive
∆WZV ∆YZV SAS postulate
RV TV Given
∆RVS ∆TVS Perpendicular bisector
SV SV Reflexive
∆RVS ∆TVS SAS postulate
SR ST CPCTC
∆RST Isosceles triangle
Prove that AB││DE
No 30 Page 295
Answer
Statements Reasons
BE DA Definition of regular octagon
<BEA <DAE Alternate interior angle
EA AE Reflexive
∆ABE ∆EDA SAS Postulate
AB ││ DETheorem 5-2(If two lines are cut by a transversal and a pair of alternate interior angles are congruent, then the lines are parallel)
Plan : Draw AE
Inscribed in a regular octagon is a star polygon. Find m<ABC. Prove that your answer is correct.
No 29 Page 295
Answer
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
XY ││ BA Theorem 5-2
Plan : Draw XA and YB intersecting at T
………AnswerStatements 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
Given : ∆ABC is isosceles with AB AC,
<AED <BProve : BCDE is a trapezoid with BE CD
No 16 Page 291
AnswerStatements Reasons
<AED <B Given
ED ││ BCTheorem 5-1(if two lines are cut by a transversal and a pair of corresponding angles are congruent, then the line are parallel)
BCDE is a trapezoid Definition of trapezoid(Trapezoid is a quadrilateral with exactly one of parallel side)
The figures shown are two overlapping rectangles. Find the sum, a+b+c+d.
No 9 Page 298
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)