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Let $l$ be a line and $P$ be a point not on $l$. Through $P$, draw a line $m$ parallel to $l$. Now join $P$ to any point $Q$ on $l$. Choose any other point $R$ on $m$. Through $R$, draw a line parallel to $PQ$. Let this meet $l$ at $S$. What shape do the two sets of parallel lines enclose?

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:45

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Steps of construction:Draw a line l, take a point A on it.Take a point P, not on l, and join A to P.Taking A as a center and with a convenient radius draw an arc cutting l at B and AP at C.Taking P as the center and with the ... Read More

Construct $∆XYZ$ in which $XY=4.5\ cm,\ YZ=5\ cm$ and $ZX=6\ cm$.

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:44

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Follow the steps given below:Draw a line segment YZ of length 5 cm.From Y, we need a point X at a distance of 4.5 cm. So, with Y as the center, draw an arc with a radius of 4.5 cm. From Z, point X is at a distance of 6 ... Read More

Construct an equilateral triangle of side $5.5\ cm$.

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:41

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Given: An equilateral triangle of side $5.5\ cm$.To do: To construct an equilateral triangle of side $5.5\ cm$.Steps of construction: Draw a line segment $BC$ of length $5.5\ cm$.Cut an arc of radius $5\ cm$ from point $B$ and an arc of $5.5\ cm$ from point $C$.Name the point of intersection ... Read More

Draw $∆PQR$ with $PQ=4\ cm$, $QR=3.5\ cm$ and $PR=4\ cm$. What type of triangle is this?

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:40

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Steps of construction -Draw a line segment QR of length 3.5 cm.From Q, we need a point P is at a distance of 4 cm. So, with Q as the center, draw an arc of radius 4 cm (Now P will be somewhere on this arc. Our job is to ... Read More

Construct $∆ABC$ such that $AB=2.5\ cm$, $BC=6\ cm$ and $AC=6.5\ cm$. Measure $\angle B$.

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:39

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To do: To construct $∆ABC$ such that $AB=2.5\ cm$, $BC=6\ cm$ and $AC=6.5\ cm$ and measure $\angle B$. Steps of construction -Let us draw a line segment $BC=6\ cm$.Assuming $B$ as the center, let us draw an arc of radius $2.5\ cm$.Assuming point $C$ as the center let us draw ... Read More

Construct $∆DEF$ such that $DE = 5\ cm$, $DF = 3\ cm$ and $\angle EDF = 90^{\circ}$.

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:38

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To do: To construct $∆DEF$ such that $DE = 5\ cm$, $DF = 3\ cm$ and $\angle EDF = 90^{\circ}$. Steps of construction :Let us draw a line segment $DE=5\ cm$. At the point $D$, let us draw a ray $DX$ making an angle of $90^{\circ}$ with $DE$ such that $\angle ... Read More

Construct an isosceles triangle in which the lengths of each of its equal sides is $6.5\ cm$ and the angle between them is $110^{\circ}$.

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:36

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To do: To construct an isosceles triangle in which the lengths of each of its equal sides are $6.5\ cm$ and the angle between them is $110^{\circ}$.Steps of construction:Let us draw a line segment $QR=6.5\ cm$. At the point $Q$, let us draw a ray $QX$ making an angle of ... Read More

Construct $∆ABC$ with $BC = 7.5\ cm$, $AC = 5\ cm$ and $\angle C = 60^{\circ}$.

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:35

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To do: To construct $∆ABC$ with $BC = 7.5\ cm$, $AC = 5\ cm$ and $m \angle C = 60^{\circ}$.Steps of construction :Let us draw a line segment $BC$ with the length of $7.5\ cm$. From the point $C$, let us draw a ray $CX$ making an angle of $60^{\circ}$ ... Read More

Construct $∆ABC$, given $m\angle A = 60^{\circ}$, $m\angle B = 30^{\circ}$ and $AB = 5.8\ cm$.

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:33

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To do: To construct $∆ABC$, given $m\angle A = 60^{\circ}$, $m\angle B = 30^{\circ}$ and $AB = 5.8\ cm$.Steps of construction :Let us draw a line segment $AB=5.8\ cm$. At A, draw ray AY making an angle of $60^{\circ}$ with AB such that $\angle YAB=60^{\circ}$. At $B$, let us draw ... Read More

Examine whether you can construct $∆DEF$ such that $EF = 7.2\ cm$, $m\angle E = 110^{\circ}$ and $m\angle F = 80^{\circ}$. Justify your answer.

Tutorialspoint

Tutorialspoint

Updated on 10-Oct-2022 13:35:31

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Given: $EF = 7.2\ cm$, $m\angle E = 110^{\circ}$ and $m\angle F = 80^{\circ}$.To do: To examine whether $∆DEF$ can be constructed.Solution: We know the angle sum property of a triangle which states that the sum of all angles in a triangle is always $180^{\circ}$.So, $\angle E + \angle F + \angle ... Read More

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