Constructions of Triangles

Q. Draw a triangle ABC with BC = 6 cm, AB = 5 cm and $\angle ABC={60}^o$. Then construct a triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the $\Delta ABC$.

Q.

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

Q. In construction of similar triangles, if scale factor is less than 1, then the new triangle is the given one.

1. smaller than
2. larger than
3. congruent to

Q.

Construct a $\Delta ABC$ with BC = 7 cm, $\angle B={60}^{\circ }$ and AB = 6 cm. Construct another triangle whose sides are $\frac{3}{4}$ times the corresponding sides of $\Delta ABC.$

Q.

Constructa $\Delta PQR,$ in which PQ = 6 cm, QR = 7 cm and PR = 8 cm. Then, construct another triangle whose sides are $\frac{4}{5}$ to, of the corresponding sides of $\Delta PQR$.

Q.

Construct a triangle similar to a given triangle PQR with its sides equal to 7/3 of the corresponding sides of the triangle PQR

(scale factor 7/3>1).

Q.

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are $1\frac{1}{2}$ times the corresponding sides of the isosceles triangle.

Q.

The ratio of $\frac{BC}{C{C}^{\prime }}$ is 3:5. What will the ratio of corresponding sides be if triangles ABC and A'BC' are similar? Given that BC and BC' lie
on the same ray BY.

1. 5:8

2. 3:8

3. 8:5

4. 8:3

Q.

AA postulate is used to prove the similarity of the constructed triangle.

1. True

2. False

Q. Question 5
Draw a $\Delta ABC$ in which AB = 5 cm , BC = 6 cm and $\angle ABC={60}^{\circ }$. Construct a triangle similar to ABC with scale factor $\frac{5}{7}$. Justify the construction.

Q.

Construct a $\Delta ABC$ in which AB = 6 cm, $\angle A={30}^{\circ }and\angle B={60}^{\circ }.$ Construct another $\Delta A{B}^{\prime }{C}^{\prime }\text{similar to}\Delta ABC$ with base AB' = 8 cm.

Q.

The construction method to prove similarity of the constructed triangles is proved by the AA similarity method.

1. True

2. False

Q.

$\Delta ABC$ of dimesions $AB=4cm,BC=5cm$ and ∠B= 60^o is given.
A ray $BX$ is drawn from $B$ making an acute angle with $AB$.
5 points $B_1,B_2,B_3,B_4\&B_5$ are located on the ray such that $BB1=B1B2=B2B3=B3B4=B4B5$.
$B_4$ is joined to $A$ and a line parallel to $B_{4}A$ is drawn through $B_5$ to intersect the extended line $AB$ at $A^{\prime }$.
Another line is drawn through $A^{\prime }$ parallel to $AC$, intersecting the extended line $BC$ at $C^{\prime }$.
Find the ratio of the corresponding sides of $\Delta ABC$ and $\Delta A^{\prime }B{C}^{\prime }$.

1. $4:1$

2. $4:5$

3. $1:4$

4. $1:5$

Q.

Choose the correct statement(s) from the options:

1. True

2. False

3. The basic principle used in dividing a line segment is similarity of triangles.
4. To divide a line segment , the ratio of division must be positive and rational .

Q.

Construct a triangle ABC in which BC is 3.5 cm, Angle B is ${75}^{\circ }$ and AB+AC=6.5cm

Q.

Construct a $△ABC$ in which BC = 8 CM, $\angle B={45}^{\circ }and\angle C={60}^{\circ }.$ Construct another triangle similar to $\Delta ABC$ such that its sides are $\frac{3}{5}$ of the corresponding sides of $\Delta ABC.$

Q.

Construct a triangle ABC, in which $\angle$B = 53.13°, $\angle$C = 36.87° and AB + BC+ CA = 24 cm. What type of triangle is this?

Q. AA postulate is used to prove the similarity of the constructed triangle.

1. False
2. True

Q.

AA postulate is used to prove the similarity of the constructed triangle.

1. True

2. False

Q. Solve the following inequation:
$3-x\le 5-3x,x\epsilon W$

Q. Construct a $\Delta ABC$ in which AB = 6 cm, $\angle A={30}^{\circ }and\angle B={60}^{\circ }.$ Construct another $\Delta A{B}^{\prime }{C}^{\prime }\text{similar to}\Delta ABC$ with base AB' = 8 cm.

Q. A triangle similar to given $\Delta ABC$with sides equal to $\frac{3}{4}$ of the sides of $\Delta ABC$ is constructed.

$\frac{B{C}^{\prime }}{BC}$ is equal to____.

1. $\frac{B{A}^{\prime }}{C{A}^{\prime }}$
2. $\frac{B{A}^{\prime }}{BA}$
3. $\frac{BC}{AC}$
4. $\frac{B{C}^{\prime }}{B_3{C}^{\prime }}$

Q. Let $H$ be the orthocentre of an acute-angled triangle $ABC$ and $O$ be its circumcenter. Then $\overline{HA}+\overline{HB}+\overline{HC}$

1. Is equal to $\overline{HO}$
2. Is equal to $3\overline{HO}$
3. Is equal to $2\overline{HO}$
4. Is not a scalar multiple of $\overline{HO}$ in general

Q.

AA postulate is used to prove the similarity of the constructed triangle.

1. True

2. False

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

Q. In $\Delta ABC,AB=BC=6cm$. A circle is drawn with center at B and radius 2 cm. What is the scale factor of the triangle formed by the point B and the points where the circle intersects $△ABC$?

1. $\frac{2}{3}$
2. $1$
3. $\frac{1}{3}$
4. $\frac{1}{2}$

Q. Solve: $\frac{2}{x}+\frac{2}{3y}=\frac{1}{6}\frac{3}{x}+\frac{2}{y}=0$

Q. If the similar triangle constructed is 5/3 times the given one, then 3 parts correspond to the given triangle.

1. True
2. False

Q.

A triangle ABC with sides BC = 7 cm, ∠B = 45°, ∠A = 105° is given. The image of constructing a similar triangle of ABC whose sides are 3/4 times the corresponding sides of the triangle ABC is given below. Then (A′ C′)/AC is equal to:

Q.

Construct a triangle ABC, in which $\angle$B = 60°, $\angle$C = 45° and AB + BC+ CA = 22 cm.