Exercise 13.1
Question 1
Given Any line AB and a point P outside AB.
Required. To draw a line parallel to AB and passing through the point p.
(Diagram to be added)
Steps of Construction:
1. Take any point Q on AB. Join P and Q
2. With Q as center and any suitable radius , draw an arc to meet AB at C and QP at D.
3. With P as center and some radius (as in step 2), draw an arc to meet PQ at E.
4. Measure the segment CD with compass.
5. With E as center and radius equal to CD, Draw an arc to cut the previous arc at F
6. Draw a line passing through P and E , then PF is the required line parallel to the line AB and passing through P.
Question 2
(Diagram to be added)
Steps:
1. Take any point on line L i.e Q
2. Take a line perpendicular i.e $90^{\circ}$ to line l.
3. Take a point on this perpendicular A above 3.
5cm from line l
4. Repeat the same procedure from step 2 in problem no. 1
Question 3
(Diagram to be added)
Step:
1. Repeat the same procedure in pb.1
2. After the steps followed in pb. Now draw a line PQ by joining P and Q, Q is a point on line l
3. Now for this line PQ, Draw a line parallel to RS wit hwith same steps followed in problem no.1
The parallel line represent a rectangle , '' parallelogram
Question 4
(i) (Diagram to be added)
1. Draw a line segment AC = 7cm
2. With A as center and radius 5cm = AB, draw an arc
3. With C as center and radius 6cm =BC , Draw an arc to cut the previous arc at B.
4. Join AB and BC. Then ABC is the required triangle .
(ii) (Diagram to be added)
1. Draw a line segment of length AC= 6cm
2. With A as center and radius 4.5cm = AB, Draw an arc
3. With C as center and radius 5cm = BC, Draw an arc to cut the previous arc at B
4. Join AB and BC. Then ABC is required Triangle .
Question 5
(Diagram to be added)
1. Draw a line segment of length PQ = 5.4 cm
2. With P as center and radius 4.7cm = PR draw an arc
3. With Q as center and radius , = 4.7cm = QR , draw an arc to cut the previous arc at B .
4 . Join PR and QR. Then PQR is required is O triangle .
Question 6
(Diagram to be added)
1. Draw a line segment LM of length 5.3cm
2. With L as center and radius 5.3cm, draw an arc.
3. With M as center and radius= 4.5 cm . Draw an arc to art the previous arc at A.
4. Joint LN and MN, then LMN is the required equilateral triangle with side 5.3cm
Question 7
(Diagram to be added)
1. Draw a line segment AC of length 6.5cm
2. With A as center and radius 2.5cm draw an arc
3. With C as center and radius 6cm draw an arc to cut the previous arc at B.
4. Joint AB and BC , then ABC is the required triangle
∴ $\angle A B C=90^{\circ}$; right angled triangle
Question 8
(Diagram to be added)
1. Draw a line segment of length QR 5.5cm
2. With center Q and radius 3cm, Draw an arc
3. At Q , constant $\angle P Q R=60^{\circ}$
4. The point which the arc cut is P. Joint p and R
5. Then the required triangle is obtained
Question 9
(Diagram to be added)
1. Draw a line segment DE of length 5cm
2. At D, constant $\angle E D F=90^{\circ}$
3. With D as center and radius 3cm, draw an arc to meet at F.
4. Join EF, then DEF is the required triangle
Question 10
(Diagram to be added)
1. Draw a line segment of length 6.5cm
2. At A, Draw $\angle B A C=110^{\circ}$ (By using protector)
3. With A as center and radius 6.5cm Draw an arc to meet AP at B.
4. Join , BC then ABC is the required isosceles triangle with given measurements on measuring $\angle A B C$ and $\angle B C A$ by protector we find that
$\angle A B C=35^{\circ}$ and $\angle BcA=35^{\circ}$
Question 11
(Diagram to be added)
1. Draw a line segment XY of length 6cm
2. At constant $\angle x=30^{\circ} .$
3. At Y , Constant $\angle Y=110^{\circ}$
4. Let rays XB and AY intersect at Z , Then XYZ is the required triangle
Question 12
(Diagram to be added)
1. Draw a line segment of PQ length 4.9cm
2. At P ,Constant $\angle P=45^{\circ}$
3. At Q constant $\angle Q = 60^{\circ}$
4. Let ray PX and QY intersect at R By measuring $\angle R=75^{\circ}$
Question 13
(Diagram to be added)
1. Draw a line segment of length 4.1cm = AB
2. $\angle B$ , constant angle 90' (By using protractor)
3. With A as center and radius = 5.2cm Cut the line with an arc which intersect at c
4. Therefore the required triangle is obtained
Question 14
(Diagram to be added)
1. Draw a line segment of length 4cm =AB
2. $\angle A$, Constant angle $90^{\circ}$ By using protractor
3. Draw an arc with B as center Cut the line at C.
4. Joint B and C . Thus required is right angled triangle
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