Construction of Triangles (Special Cases)

Construct an equilateral triangle $XYZ$of side $5 cm$ and construct another triangle similar to $△XYZ$, such that each of its sides is $\frac{4}{5}$ of the sides of $△XYZ$.

Construct a segment of a circle on a chord of length $7 \mathrm{cm}$ and containing an angle of $60°$

Construct a segment of a circle on a chord of length $8 \mathrm{cm}$ and containing an angle of $65°$

Is it possible to construct triangles with the given measurement $\left(4 \mathrm{cm}, 5 \mathrm{cm}, 6 \mathrm{cm}\right)$

What is the measure of the side of an equilateral triangle constructed rounded off to one decimal place in $\mathrm{cm}$, if each of whose altitudes measures $5.4 \mathrm{cm}$?

Constructing a triangle $\mathrm{X}\mathrm{Y}\mathrm{Z}$ in which $\mathrm{\angle }\mathrm{Y}=30°, \mathrm{\angle }\mathrm{Z}=90°$ and $\mathrm{X}\mathrm{Y}+\mathrm{Y}\mathrm{Z}+\mathrm{Z}\mathrm{X}=11 \mathrm{c}\mathrm{m}$ is possible.

Construction of $△\mathrm{PQR}$, in which $\mathrm{PQ}-\mathrm{PR}=2.4 \mathrm{cm}$, $\mathrm{QR}=6.4 \mathrm{cm}$ and $\angle \mathrm{PQR}=55°$ is possible.

A triangle, $△ABC$, with $\angle B=70°, \angle C=60°$ and $AB+BC+AC=11.2 \mathrm{cm}$ can be constructed.

We can construct a $△ABC$ in which $\angle B=45°, \angle C=60°$ and the perpendicular from the vertex $A$ to base $BC$ is $4.5 \mathrm{cm}$.

A triangle can be constructed in which $\mathrm{AC}=7 \mathrm{cm}, \angle \mathrm{C}=30°$ and $\mathrm{BC}-\mathrm{AB}=5 \mathrm{cm}$.

If all the angles of a triangle are given, we can construct a unique triangle.

Which of these triangle can be constructed?

We can construct a right triangle whose one side is $3.5 \mathrm{cm}$ and the sum of the other side and the hypotenuse is $5.5 \mathrm{cm}$.

The incorrect step(s) of construction of a $△ABC$ whose perimeter is $11.6 \mathrm{cm}$ and the base angles are $45°$ and $60°$ is/are

What is the measure of the side of an equilateral triangle constructed rounded off to one decimal place in $\mathrm{cm}$, if each of whose altitudes measures $5.4 \mathrm{cm}$?

We can construct a triangle whose perimeter is $10.4 \mathrm{cm}$ and the base angles are $45°$ and $120°$.

We can construct a right triangle whose base is $12 \mathrm{c}\mathrm{m}$ and sum of its hypotenuse and other side is $18 \mathrm{c}\mathrm{m}$.

We can construct an equilateral triangle, given its side.

A/An _____ Triangle can be constructed when the length of only one side is given.

Steps of construction of triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ in which $\mathrm{B}\mathrm{C}=8 \mathrm{c}\mathrm{m}, \mathrm{\angle }\mathrm{B}=45°$ and $\mathrm{A}\mathrm{B}-\mathrm{A}\mathrm{C}=1 \mathrm{c}\mathrm{m}$ are given below.

$\text{Step} 1\text{:}$ Draw $\mathrm{B}\mathrm{C}=8 \mathrm{c}\mathrm{m}$.

$\text{Step} 2\text{:}$ Construct $\mathrm{\angle }\mathrm{C}\mathrm{B}\mathrm{X}=45°$

$\text{Step} 3\text{:}$ Cut off $\mathrm{B}\mathrm{P}=9 \mathrm{c}\mathrm{m}$ on $\mathrm{BX}$. Join $\mathrm{C}\mathrm{P}$.

$\text{Step} 4\text{:}$ Draw perpendicular bisector for $\mathrm{P}\mathrm{C}$, meeting $\mathrm{BC}$ produced at $\mathrm{A}$.

$\text{Step} 5\text{:}$ Join $\mathrm{A}\mathrm{C}$. Then $△\mathrm{A}\mathrm{B}\mathrm{C}$ is the required triangle.

Which of the above step(s) is/are incorrect?