Construction of Quadrilateral When 3 Sides and 2 Angles Are Given
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Given below are the steps for the construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, ∠A=75∘, ∠B=105∘ and ∠C=120∘. Which of the following is wrong?
1:- Draw AB = 3.5 cm.
2:- Construct ∠DAB=75∘, ∠ABC=105∘ at B.
3:- Draw BC = 6.5 cm.
4:- At D construct ∠ADC=120∘.
3
2
4
1
(i) Quadrilateral MORE
MO=6 cm
OR=4.5 cm
∠M=60∘
∠O=105∘
∠R=105∘
PL=4 cm
LA=6.5 cm
∠P=90∘
∠A=110∘
∠N=85∘
HE=5 cm
EA=6 cm
∠R=85∘
OK=7 cm
KA=5 cm
Is it possible to construct a unique quadrilateral ABCD with AB = 3.6 cm, BC = 4 cm, AD= 5 cm, ∠ABC = 80∘ and ∠ BAD = 120∘?
With the measure of an extra side, yes.
Yes, it is possible
No, two such quadrilaterals can be constructed
No, there can be infinite such quadrilaterals
Question 2
Construct the Quadrilateral TRUE
TR=3.5 cm, RU=3cm, UE=4cm, ∠R=75∘, ∠U=120∘
Construct a quadrilateral ABCD given that AB = 8 cm, BC = 8 cm, CD = 10 cm, AD = 10 cm and ∠B=45∘.
Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD= 7cm, ∠ABC= 40∘ and ∠BCD= 55∘?
Yes, it is possible
No, two such quadrilaterals can be constructed
No, there can be infinite such quadrilaterals
With the measure of an extra side, yes
Question 1
Construct the Quadrilateral DEAR where
DE=4cm, EA=5cm, AR=4.5cm, ∠E=60∘, ∠A=90∘
Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD= 7cm , ∠ ABC = 45∘ and ∠ BCD = 55∘?
Yes, it is possible
No, two such quadrilaterals can be constructed
No, there can be infinite such quadrilaterals
With the measure of one more side, yes
He is constructing as follows:
Step 1:
Step 2:
What will be step 3?
- None of the above.
Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD= 7cm, ∠ABC= 40∘ and ∠BCD= 55∘?
Yes, it is possible
No, two such quadrilaterals can be constructed
No, there can be infinite such quadrilaterals
With the measure of an extra side, yes
Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD= 7cm, ∠ABC= 40∘ and ∠BCD= 55∘?
Yes, it is possible
No, two such quadrilaterals can be constructed
No, there can be infinite such quadrilaterals
With the measure of an extra side, yes
- True
- False
If you have AB = 3 cm, BC = 4 cm, CD = 5 cm & and DA = 6 cm, can you draw the quadrilateral ABCD? If you can, will this quadrilateral be unique?
Yes; Yes
Yes; No
No; Yes
No; No
Construction of a unique quadrilateral is possible if we have a minimum measurement of 3 sides and
If you are given AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and ∠ABC = 60∘, then it is possible to draw the quadrilateral ABCD.
False
True
Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD= 7cm , ∠ ABC = 45∘ and ∠ BCD = 55∘?
Yes, it is possible
No, two such quadrilaterals can be constructed
With the measure of an extra side, yes
No, there can be infinite such quadrilaterals
- RS
- PR
- PQ
- QR
Is it possible to construct a unique quadrilateral ABCD with AB = 3.6 cm, BC = 4 cm, AD= 5 cm, ∠ABC = 80∘ and ∠ BAD = 120∘?
Yes, it is possible
No, two such quadrilaterals can be constructed
No, there can be infinite such quadrilaterals
With the measure of an extra side, yes.
In a quadrilateral PQRS, PQ = 3 cm, QR = 4 cm and PS = 5 cm. Also, ∠SPQ = 70∘ and ∠PQR = 90∘. Which of the following options is the approximate value of ∠QRS?