Construction of an Isosceles Triangle

Mathematics – VII

About Lesson

Let us assume the base to be 5.5cm and base angle to be 50°

∴, AB = 5.5 cm and ∠B = 50°

We know that,

In an isosceles triangle, opposite sides are equal and opposite angles are equal.

So, ∠B = ∠A = 50° and AC = BC

Steps of construction:

Step 1: Draw base AB = 5.5cm.

Step 2: At vertex B, Draw a ray constructing angle of 50°.

Step 3: Now draw another ray at A constructing an angle of 50°

Step 4: Mark the point of intersection as C.

ABC is the required triangle.

Construct an isosceles triangle when vertical angle and an altitude are given.

Construct an isosceles triangle whose altitude is $4 c m$ and vertex angle is $8 0^{\circ}$

Steps of construction

Draw a line segment $X Y$ .
Take a point $M$ on $X Y$ and draw a line $M P ⊥ X Y$ .
With $M$ as center and radius $4 c m$ , draw an arc cutting $M P$ at $A$ .
Construct $B$ and $C$ on $X Y$ such that $∠ M A B = 8 0^{\circ} / 2 = 4 0^{\circ}$ and $∠ M A C = 8 0^{\circ} / 2 = 4 0^{\circ}$ .

Then $A B C$ is the required triangle.

solution

Steps of construction

Draw the base line of the given length.
Next we bisect the base line. See bisecting a line if you are unsure on how to do this. Extend the bisector if necessary. We bisect this because the apex of an isosceles triangle is always directly above the midpoint of the base line. Of course it can be anywhere along this line but we are also given the altitude.
Step the altitude off along the bisector to give you point C. Join Point A to C and Point B to C, creating an isosceles triangle with the specified properties.