Construction of Triangles Given 2 Sides and 1 Angle

Q.

Construct a triangle ABC in which BC is 8 cm, Angle B is ${75}^{\circ }$ and AB + AC = 15cm by using method of perpendicular bisector. [4 MARKS]

Q.

Construct a triangle $\mathrm{XYZ}$ in which $\angle \mathrm{Y}=30°$, $\angle \mathrm{Z}=90°$ and $\mathrm{XY}+\mathrm{YZ}+\mathrm{ZX}=11\mathrm{cm}$.

Q.

$△$ABC is constructed such that AB = 4 cm, BC = 5 cm and $\angle$A = 70${}^{\circ }$. Taking side BC as base, another triangle BCD is constructed such that length of side BD is 3 cm and length of side CD is 3 cm. Then $\angle$DBC + $\angle$DCB equals

1. 58${}^{\circ }$

2. 68${}^{\circ }$

3. 78${}^{\circ }$

4. 88${}^{\circ }$

Q. In which of the following, unique $△$ ABC cannot be constructed with the given information? Assume AB = 5 cm for each of the options.

1. BC = 4 cm, CA = 3 cm
2. $\angle A={60}^{\circ }$, $\angle B={30}^{\circ }$
3. $\angle C={60}^{\circ }$, BC = 3 cm
4. BC = 7 cm , $\angle B={30}^{\circ }$

Q.

$△$ABC is constructed such that AB = 5.5 cm, BC = 6 cm and $\angle$A = 60${}^{\circ }$. Then the difference between the measure of $\angle$B and $\angle$C is

1. 7${}^{\circ }$

2. 12${}^{\circ }$

3. 14${}^{\circ }$

4. 17${}^{\circ }$

Q.

Draw a triangle $\mathrm{ABC}$ with side $\mathrm{BC}=6\mathrm{cm},\mathrm{AB}=5\mathrm{cm}$ and $\angle \mathrm{ABC}=60°$. Then construct a triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the triangle $\mathrm{ABC}$. Give the justification of the construction

Q.

Construct a triangle having two sides as 6 cm & 1 cm and a non - included angle as ${60}^{\circ }.$ How many such triangle is possible ?

1. 2

2. 1

3. 3

4. 0

Q.

State whether the following statements are true (T) or false (F):

(iii) The number of angles in a triangle is a variable.

1. True
2. False

Q. Construct a triangle having two sides as 5 cm and 4 cm and one non- included angle as ${30}^{\circ }.$ How many such triangle can be drawn ?

1. 1
2. 2
3. 3
4. 4

Q. Construct $\Delta ABC$ in which AB = 5 cm, $\angle B={45}^o$ and $BC=6cm$.

Q.

$△$ABC is constructed such that AB = 4 cm, BC = 4.5 cm and $\angle$A = 30${}^{\circ }$. Then the length of side AC is

1. 5.5 cm

2. 6.3 cm

3. 7.5 cm

4. 8.4 cm

Q. Draw the following triangles and construct circumcircles for them.
In $△ABC,AB=6cm,BC=7cm$ and $\angle A={60}^o$

Q. Construct a triangle $PQR$ in which $QR=6cm,\angle Q={60}^{o}andPR-PQ=2cm$.

Q.

Which among the given options must be the length of side AC for triangle construction to be possible, if length of side AB is 6 cm and $\angle$ B = 70${}^{\circ }$?

1. 6 cm

2. 3 cm

3. 4 cm

4. 5 cm

Q.

A triangle is constructed such that one of its side 10 cm, another side is of length 9 cm and the angle opposite to the side of length 9 cm is 60${}^{\circ }$. This construction results in the formation of two triangles. Let us call the third vertex of the smaller triangle as $C_1$ and the third vertex of the bigger triangle as $C_2$, as shown in the image below.

(image here)

Then x${}^{\circ }$ + y${}^{\circ }$ equals

1. 89${}^{\circ }$

2. 78${}^{\circ }$

3. 82${}^{\circ }$

4. 86${}^{\circ }$

Q.

A triangle is constructed such that one of its side 8 cm, another side is of length 5.5 cm and the angle opposite to the side of length 5.5 cm is 40${}^{\circ }$. This construction results in the formation of two triangles. Let us call the third vertex of the smaller triangle as $C_1$ and the third vertex of the bigger triangle as $C_2$, as shown in the image below.

Then x${}^{\circ }$ + y${}^{\circ }$ equals

1. 120${}^{\circ }$

2. 140${}^{\circ }$

3. 160${}^{\circ }$

4. 180${}^{\circ }$

Q. Suppose we have to cover the xy-plane with identical tiles such that no two tiles overlap and no gap is left between the tiles. Suppose that we can choose tiles of the following shapes: equilateral triangle, square, regular pentagon, regular hexagon. Then the tiling can be done with tiles of

1. All four shapes
2. Exactly three of the four shapes
3. Exactly two of the four shapes
4. Exactly one of the four shapes

Q. The length of an arc of a circle of radius 5 cm subtending a central angle measuring ${15}^{\circ }=\frac{a\pi }{12}$. Find $a$.

Q. Construct a triangle ABC in which BC = 8cm , $\angle B$ = ${45}^0$ and $AB-AC=3.5$ cm .

Q.

A triangle is constructed such that the length of its two sides are 7 cm and 2.5 cm and the angle opposite to the side of length 2.5 cm is 15${}^{\circ }$. This construction results in the formation of two triangles. Then the perimeter of the so formed obtuse angled triangle is

1. 9.5 cm

2. 11 cm

3. 20.5 cm

4. 18 cm

Q. Draw a triangle $PQR$ in which $PQ=7cm,QR=3cm,RP=4cm$. Is the construction of triangle possible?

Q. Construct a triangle ABC with AB = 7cm, BC = 6.5 cm and $\angle CAB={60}^{\circ }$. Measure the length of AC (in cm)

1. $7.7$ cm
2. $6.7$ cm
3. $7.6$ cm
4. $5.7$ cm

Q. Construct a $△ABC$ in which base $\angle B={60}^0$, height corresponding to base $BC=4.3$cm and length of median corresponding to side $AB=6$ cm.

Q. $ABCD$ is a parallelogram in which $BC$ is proved to $E$ such that $CE=BC$. $AE$ intersect $CD$ at $F$.
Prove that If the area of $△DFB=3c{m}^2$, find the area (in $c{m}^2$) of $|{|}^{gm}ABCD$.

Q. At 3 o'clock, the angle formed between the two hands of a clock is

1. right
2. acute
3. obtuse
4. left

Q.

Construction of a triangle with the following specifications is possible.

Length of side AB = 8 cm, Length of side BC = 3 cm and $\angle$A = 40${}^{\circ }$.

1. True

2. False

Q. draw a triangle ABC of
AB = 5cm
$\angle B={90}^{\circ }$ and BC $=5cm$

Q. Draw and locate the centroid of triangle $LMN$ with $LM=5.5cm,\angle M={100}^{\circ },MN=6.5cm$

Q.

Find the midpoint of a line segment of AB = 8 cm , With AB as base construct an isoceles triangle of 2 equal angles having value of ${40}^{\circ }$ [3 MARKS]

Q.

Draw a triangle $ABC$ in which $AB=4.5cm,$ $BC=6cm$ and $\angle B={80}^{\circ }$.