Question

Construct \[\Delta XYZ\] , such that \[YZ = 7.4cm\] , \[\angle XYZ = {45^ \circ }\] and \[XY - XZ = 2.7cm\]

Answer 1

Hint: Here we will first draw the base and then we will draw the given angle and use the given condition to draw the other two sides of the triangle.

Complete step-by-step answer:
Draw the line segment YZ of length 7.4 cm as shown in the following figure:-

Draw ray YP, such that \[\angle ZYP = {45^ \circ }\]

Now it is given that \[XY - XZ = 2.7cm\]
Mark point On ray YP such that length of (YT) = 2.7 cm.
Hence, \[XY - TX = 2.7cm\]
Therefore, \[TX = XZ\]

Join points T and Z
Also, since \[TX = XZ\]
Hence, X is the perpendicular bisector of YZ.

Join the points X and Z.

Therefore, the above figure is the required triangle.

Note: Students should use compass and scale for perfect measurement and arcs a an accurate
distance to get the desired triangles.
Also, the bisector of a line segment divides it into two equal parts.