Construction Of Quadrilaterals
Class 8th Mathematics (old) MHB Solution
- One side and one diagonal of a rhombus ABCD are 4.5cm and 5.5cm respectively.…
- In □DEFG l(DE) = 5cm, l(EF) = 6cm, l(FG) = 7cm, l(DG) = 3 cm and l(DF) = 9cm.…
- In a parallelogram PQRS l(PQ) =3.5cm, l(QR)=4.5cm, and l(PR) = 6.5cm Draw the…
- In □DEFG l(EF) = 3.5cm, l(DE) = 5.5cm, l(DF) =7.5cm, l(DG) = 5cm l(EG) = 8cm.…
- In □GOLD l(OD) = 10cm, l(OL) = 7.5cm, l(LD) = 5cm, l(GD) = 4cm, l(GL) = 6cm.…
- In □PLAY, l(PL) = 4.5cm, l(LA) = 6.5cm l(PY) = 5.5cm, l(PA) =8.5cm, l(LY)=7.5cm…
Exercise 52
Question 1.Draw the Quadrilaterals of the following measures.
One side and one diagonal of a rhombus ABCD are 4.5cm and 5.5cm respectively.
Answer:
Steps of construction:
i: Draw a line segment BD of 5.5cm.
ii: With a 4.5cm as radius from D draw an arc.
iii: With 4.5cm as radius B cut the arc drawn in step 2. Let that point of intersection be A.
iv: Join AD and AB.
v: With a 4.5cm as radius from B draw an arc to the opposite side of BD.
vi: From D take 4.5cm as radius and cut the arc drawn in step 4. Let the point of intersection be C.
vii: Join CD and BC.
viii: ABCD is the required quadrilateral.
Question 2.
Draw the Quadrilaterals of the following measures.
In □DEFG l(DE) = 5cm, l(EF) = 6cm, l(FG) = 7cm, l(DG) = 3 cm and l(DF) = 9cm.
Answer:
Steps of construction:
i: Draw a line segment DF of 9cm.
ii: With a 5cm as radius from D draw an arc.
iii: With 6cm as radius from F cut the arc drawn in step 2. Let that point of intersection be E. Join DE and EF.
iv: With a 7cm as radius from F draw an arc to the opposite side of DF.
v: From D take 3cm as radius and cut the arc drawn in step 4. Let the point of intersection be G.
vi: Join DG and FG.
vii: DEFG is the required quadrilateral.
Question 3.
Draw the Quadrilaterals of the following measures.
In a parallelogram PQRS l(PQ) =3.5cm, l(QR)=4.5cm, and l(PR) = 6.5cm
Answer:
Steps of construction:
i: Draw a line segment PR of 6.5cm.
ii: With a 4.5cm as radius from R draw an arc.
iii: With 3.5cm as radius from P cut the arc drawn in step 2. Let that point of intersection be Q.
iv: Join PQ and QR.
v: With a 4.5cm as radius from P draw an arc to the opposite side of BD.
vi: From R take 3.5cm as radius and cut the arc drawn in step 4. Let the point of intersection be S.
vii: Join PS and SR.
viii: PQRS is the required quadrilateral.
Exercise 53
Question 1.Draw quadrilaterals of the following measures.
In □DEFG l(EF) = 3.5cm, l(DE) = 5.5cm, l(DF) =7.5cm, l(DG) = 5cm l(EG) = 8cm.
Answer:
Steps of construction:
i: Draw a line segment GE 8cm.
ii: With 5.5cm from G draw an arc.
iii: From E take radius of 4.5cm and cut the arc drawn in step 2. Let the point of intersection be D.
iv: Take 7.5 cm from D draw an arc on opposite side of GE.
v: Take 3.5cm radius from E and cut the arc drawn in step 4. Let the point of intersection of arcs be F.
vi: Join GF.
vii: DEFG is the required quadrilateral.
Question 2.
Draw quadrilaterals of the following measures.
In □GOLD l(OD) = 10cm, l(OL) = 7.5cm, l(LD) = 5cm, l(GD) = 4cm, l(GL) = 6cm.
Answer:
Steps of construction:
i: Draw a line segment GL 6cm.
ii: With 4 cm radius from G draw an arc.
iii: From L take radius of 5cm and cut the arc drawn in step 2. Let the point of intersection be O.
iv: Take 10 cm from O draw an arc.
v: Take 7.5 cm radius from L and cut the arc drawn in step 4. Let the point of intersection of arcs be D.
vi: Join GD.
vii: GOLD is the required quadrilateral.
Question 3.
Draw quadrilaterals of the following measures.
In □PLAY, l(PL) = 4.5cm, l(LA) = 6.5cm l(PY) = 5.5cm, l(PA) =8.5cm, l(LY)=7.5cm
Answer:
Steps of construction:
i: Draw a line segment LY 7.5cm.
ii: With 5.5 cm from Y draw an arc.
iii: From L take radius of 4.5cm and cut the arc drawn in step 2. Let the point of intersection be A.
iv: Take 8.5 cm from P draw an arc.
v: Take 6.5cm from L and cut the arc drawn in step 4. Let the point of intersection of arcs be Y.
vi: Join AY.
vii: PLAY is the required quadrilateral.
Exercise 54
Question 1.Draw quadrilaterals of the following measures.
In □DEFG, l(DE) =4.5 cm, l(EF) = 6.5cm m∠D = 65°, m∠E = 100°, m∠F = 60°.
Answer:
Steps of construction:
i: Draw a line segment DE = 4.5cm.
ii: Construct an angle of 65° at D and produce the side DG’.
iii: Construct an angle of 100° at E and produce EF’.
iv: Take radius 6.5cm and cut an arc at EF’ and mark this point as F.
v: Now, construct an angle of 60° at F and produce EG such that EG cuts DG’. Mark intersection point as G.
vi: DEFG is required quadrilateral.
Question 2.
Draw quadrilaterals of the following measures.
In □MTSN l(MT) = 4cm, l(TS) = 5cm m∠M=50°, m∠T = 110°, m∠S = 70°.
Answer:
Steps of construction:
i: Draw a line segment MT = 4cm.
ii: Construct an angle of 50° at M and produce the side MN’.
iii: Construct an angle of 110° at T and produce TS’.
iv: Take radius 5cm and cut the arc at TS’ and mark this point as S.
v: Now, construct an angle of 70° at S and produce SQ’ such that SQ’ cuts MN’. Mark intersection point as N.
vi: MTSN is required quadrilateral.
Question 3.
Draw quadrilaterals of the following measures.
In □XYZW, l(XY) = 5.5cm, l(XW) =3cm, m∠X = 70°, m∠Y = 95°, m∠Z =85°
Answer:
∠X + ∠Y +∠Z + ∠W = 360°
⇒ 70° + 95° + 85° + ∠W = 360°
⇒ 250 +∠W = 360°
⇒∠W = 360° -250°
⇒ ∠W = 110°
Steps of construction:
i: Draw a line segment XY = 5.5cm.
ii: Construct an angle of 95° at Y and produce the side YZ’.
iii: Construct an angle of 70° at X and produce XW’.
iv: Take radius of 3cmand cut XW’ and mark that point as W.
v: Now, construct an angle of 110° at Z and produce ZP such that ZP cuts XW’ and mark this point as W.
vi: WXYZ is required quadrilateral.
Exercise 55
Question 1.Draw quadrilaterals of the following measures.
In □TYRE l(TY) = 3.5cm, l(YR) = 5cm, l(RE) = 4.5 cm, m∠Y = 60°, m∠R = 120°.
Answer:
Steps of construction:
i: Draw a line segment of TY =3.5cm
ii: At vertex Y of TY segment draw a line constructing an angle of 60°.
iii: With Y as centre and radius 5 draw an arc to cut YR’.
iv: At vertex R of segment YR draw a line constructing an angle of 120°.
v: With R as centre and radius 4.5cm draw an arc to cut RE’.
vi: Join TE
vii: TYRE is required quadrilateral
Question 2.
Draw quadrilaterals of the following measures.
In □KING, l(KI) =3.5cm, l(IN) = 5.5cm, l(NG) = 5cm, m∠N = 75°, m∠I = 115°.
Answer:
Steps of construction:
i: Draw a line segment of GN =5cm
ii: At vertex N of GN segment draw a line constructing an angle of 75°.
iii: With N as centre and radius 5.5 draw an arc to cut NI’ and mark that arc as I.
iv: At vertex I of segment NI draw a line constructing an angle of 115°.
v: With I as centre and radius 3.5cm draw an arc to cut RE’ and mark as K. Join KG
vi: KING is required quadrilateral.
Question 3.
Draw quadrilaterals of the following measures.
In □RDTG, l(RD) = 6cm, l(DT) =4cm, l(TG) = 4cm, m∠D = 100°, m∠T = 90°
Answer:
Steps of construction:
i: Draw a line segment of Gt =4cm
ii: At vertex T of GT segment draw a line constructing an angle of 90°.
iii: With T as centre and radius 5.5 draw an arc to cut TD’ and mark that arc as D.
iv: At vertex D of segment DR’ draw a line constructing an angle of 100°.
v: With D as centre and radius 3.5cm draw an arc to cut DR’ and mark as R.
vi: Join RG
vii: RDTG is required quadrilateral
