Tag: construction of triangles - i

The perimeter of a triangle is $45\ cm$. Length of the second side is twice the length of first side. The third side is $5$ more than the first side. Find the length of each sides and construct the triangle made by these three sides.

Construct a triangle $ABC$ in which $AB = 5 cm$ and $BC = 4.6 cm$ and $AC = 3.7 cm$
Steps for the construction is given in jumbled form.Choose the appropriate sequence for the above
1) With radius as $5\ cm$ from $C$, cut an arc.
2)They arcs will intersect at point $A$. Join $AB$ and $AC$. $ABC$ is the required triangle.
3)Draw a line segment $BC = 4\ cm.$
4)With radius as $3$ cm from $B$, cut the arc. 

Construct an isosceles $\triangle  XYZ,$ where $YZ=5$ units and $\angle XYZ=35^{o}$. Also, find the measure of $\angle YXZ$.

Construct an isosceles $\triangle  ABC,$ where base $AB=7\ cm$ and $\angle ABC=50^{o}$. Also, find the measure of $\angle ACB$.

For construction of a $\triangle PQR$, where $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the fourth step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass .
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle. 
5. Draw the base side $ QR = 6\  cm $.

State the following statement is True or False
In a right angle triangle $ABC$ such as $AC=5 cm ,BC=2 cm$ , $\angle B=90^o$
Then the length of $AB$ after construction is $7$cm

For construction of a $\triangle PQR$, where $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the second step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle. 
5. Draw the base side $ QR = 6\  cm $.

For construction of a $\triangle PQR$, when $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the fifth step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass.
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle. 
5. Draw the base side $ QR = 6\  cm $.

For construction of a $\triangle PQR$, where $\displaystyle QR=6\ cm, PR=10\ cm$ and $\angle Q=90^{\circ}$, its steps for construction is given below in jumbled form. Identify the first step from the following.

1. At point $ Q $, draw an angle of $ {90}^{\circ} $.
2. From $ R $ cut an arc of length $ PR = 10.0 \ cm $ using a compass .
3. Name the point of intersection of the arm of the angle $ {90}^{\circ} $ and the arc drawn in step 3, as $ P $.
4. Join $P $ to $ Q $ . $ PQR $ is the required triangle. 
5. Draw the base side $ QR = 6\  cm $.

Construct a triangle $ABC$, in which $AB = 5.5 cm, AC = 6.5 cm$ and $\angle BAC = 70^{\circ}$.
Steps for its construction is given in a jumbled form.Identify its correct sequence.
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 $AB = 5.5cm$.