Question 1
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.
$\begin{matrix} T r i a n g l e & G i v e n m e a s u r e m e n t s 1. & Δ A B C & m ∠ A = 85^{\circ} & m ∠ B = 115^{\circ} & A B = 5 c m \end{matrix}$

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Solution

In $Δ$ ABC, $m ∠ A = 85^{\circ}, m ∠ B = 115^{\circ}, A B = 5 c m$
Construction of $Δ$ ABC is not possible because $m ∠ A = 85^{\circ} + m ∠ B = 200^{\circ}$ , and we know that sum of angles of a triangle should be $180^{\circ}$ .

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Similar questions

\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}

\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?

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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