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)