Question

*While constructing a triangle when its base, an angle adjacent to the base and the sum of the lengths of remaining sides is given which theorem do we use?*

1️⃣ angle bisector theorem
2️⃣ perpendicular bisector theorem
3️⃣ theorem of isosceles triangle
4️⃣ theorem of centroid of a triangle.​

Answer 1

Given : Constructing a triangle when its base, an angle adjacent to the base and the sum of the lengths of remaining sides is given

To Find : which theorem do we use?*

1️⃣ angle bisector theorem

2️⃣ perpendicular bisector theorem

3️⃣ theorem of isosceles triangle

4️⃣ theorem of centroid of a triangle.​

Solution:

perpendicular bisector theorem  is used

An Example :

triangle abc in which b=150° bc=5cm and ab+ac=7.3cm  

Step 1: Draw a line segment BC 5 cm.

Step 2 : Draw ∠B =150° using protractor and draw a ray BX.

Step 3 : With Center B and radius 7.3 cm, make an arc which intersects BX at D.

Step 4 : Join CD

Step 5 : Draw a perpendicular bisector of segment DC it intersect the ray BX at point A.

Step 6 : Join C to A

Triangle is constructed

perpendicular bisector theorem

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