Following are the measures of certain sides and angles of triangle. You have to identify which cannot be constructed and say why it cannot be constructed. Now, construct the triangle if possible.
In $△ PQR, PQ = 2 cm, QR = 4 cm, PR = 2 cm$

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Solution

Given, in $△ PQR, PQ = 2 cm, QR = 4 cm, PR = 2 cm$
Since the sum of lengths of two sides of a triangle is always greater than the length of the third side.
Here, $PQ + PR = QR$
i.e. $PQ + PR$ is not greater than $QR$ .
Thus, $△ PQR$ cannot be constructed.

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Q. Question 7
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 7. & Δ X Y Z & X Y = 3 c m & Y Z = 4 c m & X Z = 5 c m \end{matrix}

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

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Following are the measures of certain sides and angles of triangle. You have to identify which cannot be constructed and say why it cannot be constructed. Now, construct the triangle if possible.In △PQR,PQ=2cm,QR=4cm,PR=2cm

Given, in △PQR,PQ=2cm,QR=4cm,PR=2cmSince the sum of lengths of two sides of a triangle is always greater than the length of the third side.Here, PQ+PR=QRi.e. PQ+PR is not greater than QR.Thus, △PQR cannot be constructed.

Following are the measures of certain sides and angles of triangle. You have to identify which cannot be constructed and say why it cannot be constructed. Now, construct the triangle if possible.
In $△ PQR, PQ = 2 cm, QR = 4 cm, PR = 2 cm$

Given, in $△ PQR, PQ = 2 cm, QR = 4 cm, PR = 2 cm$
Since the sum of lengths of two sides of a triangle is always greater than the length of the third side.
Here, $PQ + PR = QR$
i.e. $PQ + PR$ is not greater than $QR$ .
Thus, $△ PQR$ cannot be constructed.