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

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Solution

To construct: A triangle whose sides are XY=3cm, YZ = 4cm and XZ=5cm.
Steps of construction:

(a) Draw a line segment ZY = 4cm.
(b) Taking Z as center and radius 5cm, draw an arc.
(c) Taking Y as centre and radius 3cm, draw another arc.
(d) Both arcs intersect at point X.
It is the required triangle XYZ.

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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 2. & Δ P Q R & m ∠ Q = 30^{\circ} & m ∠ R = 60^{\circ} & Q R = 4.7 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?

X Y Z

X Y = 7.5 c m

Y Z = 6.2 c m

X Z = 5.8 c m

△ X Y Z

X Y = 4 c m, y z = 6 c m

Z X = 3 c m

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