Question

Construct ΔXYZ, in which YZ = 6 cm, XY + XZ = 9 cm. ∠XYZ = 50°.

Answer 1

Rough figure:

Explanation:

As shown in the rough figure, first we draw seg YZ = 6 cm of length.

Draw a ray YT making an angle of 50° with seg YZ.

Mark point W on YT such that YW = 9 cm

Now, YX + XW = YW      ...[Y-X-W]

∴ YX + XW = 9 cm       ...(i)

Given XY + XZ = 9 cm      ...(ii)

∴ YX + XW = XY + XZ        ...[From (i) and (ii)]

⇒ XW = XZ

∴ X is on the perpendicular bisector of WZ.

∴ The point of intersection of ray YT and perpendicular bisector of ray WZ is point X.

Steps of construction:

1. Draw seg YZ of length 6 cm.
2. Draw ray YT such that ∠ZYT = 50°.
3. Mark point W on ray YT such that YW = 9 cm
4. Draw seg WZ.
5. Construct the perpendicular bisector of seg WZ.
6. Name the point of intersection of ray YW and the perpendicular bisector of WZ as X.
7. Draw seg XZ.

Therefore, △XYZ is the required triangle.