Question 2
Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangle.
$\begin{matrix} T r i a n g l e & G i v e n m e a s u r e m e n t s 2. & Δ P Q R & m ∠ Q = 30^{\circ} & m ∠ R = 60^{\circ} & Q R = 4.7 c m \end{matrix}$

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Solution

To construct: $Δ$ PQR where $m ∠ Q = 30^{\circ}, m ∠ R = 60^{\circ}$ QR=4.7cm
Steps of construction:

(a) Draw a line segment QR = 4.7 cm.
(b) At point Q, draw $∠$ XQR=30 with the help of compass.
(c) At point R, draw $∠$ YRQ = 60 with the help of compass.
(d) QX and RY intersect at point P.
It is the required triangle PQR.

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\begin{matrix} T r i a n g l e & G i v e n m e a s u r e m e n t s 7. & Δ X Y Z & X Y = 3 c m & Y Z = 4 c m & X Z = 5 c m \end{matrix}

\begin{matrix} T r i a n g l e & G i v e n m e a s u r e m e n t s 5. & Δ A B C & B C = 2 c m & A B = 4 c m & A C = 2 c m \end{matrix}

Look at the given measure of sides and angles of the triangles, which of the following triangle cannot be constructed?

Statement $1$ : It is possible to construct a triangle when measurements of two sides and one angle are given.

Statement $2$ : It is possible to construct a triangle when measurements of two sides and included angle are given.

Choose the correct option.

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