Given a line segment SR of 2.5 cm. Construct a line segment PT of 2 cm parallel to SR.

Construct a $$\triangle ABC$$, when:

$$\displaystyle AB=6.0\ cm,AC=8.0\ cm$$ and $$BC=7.5\ cm.$$Type 1 if following are the steps of construction and type 0 if following are not tue steps of construction.

Steps of Construction:

(i) Draw a line segment $$PQ = 10\space\mathrm{cm}$$.

(ii) At $$P$$, draw a ray making an angle of $$30^{\circ}$$.

(iii) At $$Q$$, draw another ray making an angle of $$60^{\circ}$$ which intersects the first ray at $$R$$.

$$\triangle PQR$$ is the required triangle.

Construct a $$\triangle ABC$$ in which $$BC = 6.5\ cm, \angle ABC = 60^{\circ}, AB = 5\ cm$$. Construct a locus of points $$l_1$$ at a distance of $$3.5\ cm$$ from $$A$$. Also, construct a locus of points $$l_2$$ which is equidistant from $$AC$$ and $$BC$$. Let $$l_1$$ intersect $$l_2$$ in two points $$X$$ and $$Y$$. Measure $$XY$$.

If the stpes of construction are given as below the answer the following question:

Which is the last step of construction?

1) At $$A$$, construct a line segment $$AE$$, sufficiently large, such that $$\angle BAC$$ at $$70^\circ$$, use protractor to measure $$70^\circ$$

2) Draw a line segment which is sufficiently long using ruler.

3) With $$A$$ as centre and radius $$6.5cm$$, draw the line cutting $$AE$$ at C, join $$BC$$, then $$ABC$$ is the required triangle.

4) Locate points $$A$$ and $$B$$ on it such that $$AB = 5.5cm$$.

1) At $$A$$, construct a line segment $$AE$$, sufficiently large, such that $$\angle BAC$$ at $$70^\circ$$, use protractor to measure $$70^\circ$$

2) Draw a line segment which is sufficiently long using ruler.

3) With $$A$$ as centre and radius $$6.5cm$$, draw the line cutting $$AE$$ at C, join $$BC$$, then $$ABC$$ is the required triangle.

4) Locate points $$A$$ and $$B$$ on it such that $$AB = 5.5cm$$.

$$XY=4.5\ \text{cm}$$, $$\angle X={60 }^ { \circ }$$ and $$\angle Y={45 }^ { \circ }$$.

(i) the locus of the centres of all circles which touch $$AB$$ and $$AC$$,

(ii) the locus of the centres of all the circles of radius $$2\ cm$$ which touch $$AB$$.

Hence, construct the circle of radius $$2\ cm$$ which touches $$AB$$ and $$AC$$.

$$1.$$ Area of triangle

$$2.$$ Height of the triangle corresponding to the smallest side.

$$3.$$ Height of the triangle corresponding to the longest side.

Fill in the blank.

The longest side of a right angled triangle is called as ___________.
(i)a triangle ABC ,given AB =4 cm, BC=6 CM AND $$\angle ABC = {90^ \circ }$$

(II)a circle which passes through the points a,b,and c and mark its centre

as o.

$$YZ=5\,cm,\angle ZYX=30^{o} $$ and $$\angle YZX=75^{o}$$.

$$AB=5.4$$ cm, $$AC=5$$ cm and $$\angle A=45^{o}$$.

$$AB=6\ cm,BC=5\ cm$$ and $$CA=5\ cm$$

$$BC=4.8\ cm,AB=5.7\ cm$$ and $$\angle A=45^o$$.

$$AB=BC=5.8\ cm, $$ and $$AC=4\ cm$$

Construct $$\triangle{ABC}$$, $$AB=9$$cm ,$$BC=9$$cm and $$\angle{ABC}={45}^{\circ}$$.

Also draw a circle of radius $$2$$ cm to touch the arms of $$\angle{ACB}$$

$$a=6$$cm, $$b=8$$cm.

(Hint : Recall angle-sum property of a triangle),

$$a=3$$cm, $$b=4$$cm.

$$a=2$$cm, $$b=1.5$$cm.

$$a=8$$cm, $$b=15$$cm.

Construct $$\Delta ABC$$ where AB = 3.5 cm, BC = 6 cm and $$\angle ABC=60^{\circ }$$

Triangle $$ABC$$, in which $$AB = 5.5$$ cm, $$BC = 3.2$$ cm and $$CA = 4.8$$ cm.

a triangle $$ABC$$ in which $$AB = 5.5$$ cm, $$BC = 3.4$$ cm and $$CA = 4.9$$ cm.

Construct an isosceles $$\triangle ABC$$ when base $$BC=5.4\ cm$$ and side $$AB=6.8\ cm$$

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