By using the properties of the triangle and the above basic constructions we can construct triangles.

**Construction 1: How to construct a triangle if its base, a base angle and sum of other two sides are given?**

Given the base BC, a base angle B and the sum of other two sides AB + AC of a triangle ABC, now we need to construct it.

**Steps of Construction:**

**Step 1: **First of all, draw the base BC and at the point B make an XBC equal to the given angle.

**Step 2: **From the ray BX, cut the line segment BD = AB + AC.

**Step 3:** Join DC now which make DCY = BDC.

**Step 4: **When CY intersect BX at A then it form the required triangle i.e. ABC.

**Construction 2:** **How to construct a triangle if its base, a base angle and the difference of the other two sides are given?**

Given the base BC, a base angle i.e. B and the difference of the other two sides AB – AC or AC – AB, we need to construct the triangle ABC. There could be two cases:

**Case (i):** **If AB > AC that is AB – AC is given.**

**Steps of Construction**:

**Step 1: **Draw the base BC which is equal to a cm and at point B make an XBC = x°.

**Step 2: **From ray, BX cut the line segment BD which is equal to AB – AC.

**Step 3: **Join DC and draw the perpendicular bisector of DC.

**Step 4: **This perpendicular bisector intersects BX at a point A. By joining A to C we get the required triangle i.e. ∆ABC.

**Case (ii): If AB < AC that is AC – AB is given.**

**Steps of Construction:**

**Step 1: **Draw the base BC and at point B make an XBC.

**Step 2: **From ray, BX cut the line segment BD which is equal to AC – AB from the line BX by extending it on opposite side of line segment BC.

**Step 3: **Join DC and draw the perpendicular bisector of DC.

**Step 4: **Let PQ intersect BX at A and by joining A to C, we get the required triangle ∆ABC.

**Construction 3: How to construct a triangle if its perimeter and two base angles are given?**

Given the base angles, say B and C and BC + CA + AB, you have to construct the triangle ABC.

**Steps of Construction**:

**Step 1: **Draw a line segment XY = BC + CA + AB.

**Step 2: **Make LXY = B and MYX = C.

**Step 3: **Now bisect LXY and MYX. These bisectors will intersect at a point A.

**Step 4: **Draw perpendicular bisectors PQ of AX and RS of AY.

**Step 5: **Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.

Then ABC is the required triangle.

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