## Construct a triangle XYZ in which ∠Y = 30°,

[question] Question. Construct a triangle $X Y Z$ in which $\angle Y=30^{\circ}, \angle Z=90^{\circ}$ and $X Y+Y Z+Z X=11 \mathrm{~cm}$. [/question] [solution] Solution: The below given steps will be followed to construct the required triangle. Step I: Draw a line segment AB of 11 cm. (As $X Y+Y Z+Z X=11 \mathrm{~cm}$ ) Step II: Construct an angle, ∠PAB, of 30° at point A and an angle, ∠QBA, of 90° at point B. Step III: Bisect ∠PAB and ∠QBA. Let these bisectors intersect each other at point X. S...

## Construct a triangle PQR in which QR = 6 cm,

[question] Question. Construct a triangle $P Q R$ in which $Q R=6 \mathrm{~cm}, \angle Q=60^{\circ}$ and $P R-P Q=2 \mathrm{~cm}$ [solution] Solution: The below given steps will be followed to construct the required triangle. Step I: Draw line segment $Q R$ of $6 \mathrm{~cm}$. At point $Q$, draw an angle of $60^{\circ}$, say $\angle X Q R$. Step II: Cut a line segment $Q S$ of $2 \mathrm{~cm}$ from the line segment $Q T$ extended in the opposite side of line segment $X Q$. (As PR PQ and PR $P Q...

## Construct a triangle ABC in which BC = 8 cm,

[question] Question. Construct a triangle $A B C$ in which $B C=8 \mathrm{~cm}, \angle B=45^{\circ}$ and $A B-A C=3.5 \mathrm{~cm}$. [/question] [solution] Solution: The below given steps will be followed to draw the required triangle. Step I: Draw the line segment $B C=8 \mathrm{~cm}$ and at point $B$, make an angle of $45^{\circ}$, say $\angle X B C$. Step II: Cut the line segment $B D=3.5 \mathrm{~cm}$ (equal to $A B-A C$ ) on ray $B X$. Step III: Join DC and draw the perpendicular bisector P...

## Construct an equilateral triangle,

[question] Question. Construct an equilateral triangle, given its side and justify the construction [/question] [solution] Solution: Let us draw an equilateral triangle of side 5 cm. We know that all sides of an equilateral triangle are equal. Therefore, all sides of the equilateral triangle will be 5 cm. We also know that each angle of an equilateral triangle is 60º. The below given steps will be followed to draw an equilateral triangle of 5 cm side. Step I: Draw a line segment AB of 5 cm lengt...

## Construct the angles of the following measurements:

[question] Question. Construct the angles of the following measurements: (i) $30^{\circ}$ (ii) $22 \frac{1}{2}$ 。 (iii) $15^{\circ}$ [/question] [solution] Solution: (i) $30^{\circ}$ The below given steps will be followed to construct an angle of 30°. Step I: Draw the given ray PQ. Taking P as centre and with some radius, draw an arc of a circle which intersects PQ at R. Step II: Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point S. ...

## construct an angle of 45° at the initial point of a given

[question] Question. Construct an angle of 45° at the initial point of a given ray and justify the construction. [/question] [solution] Solution: The below given steps will be followed to construct an angle of 45°. (i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre, which intersects PQ at R. (ii) Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S. (iii) Taking S as centre and with the same radius as before...

## Construct an angle of 90° at the initial point of a given ray and justify the construction.

[question] Question. Construct an angle of 90° at the initial point of a given ray and justify the construction. [/question] [solution] Solution: The below given steps will be followed to construct an angle of 90°. (i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre, which intersects PQ at R. (ii) Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S. (iii) Taking S as centre and with the same radius as before...