Construction 11.4 :
To construct a triangle, given its base, a base angle and sum of other two sides.
Given base BC,
a base angle ∠B
and the sum AB + AC,
we need to construct Δ ABC
Steps of Construction:
Draw base BC
2. Now, let’s draw ∠ B
Construct angle B from point B.
Let the ray be BX
3. Open the compass to length AB + AC.
From point B as center, cut an arc on ray BX.
Let the arc intersect BX at D
4. Join CD
Now, we will draw perpendicular bisector of CD
6. Mark point A where perpendicular bisector intersects BD
Join AC
∴ Δ ABC is the required triangle
Check Construction 11.2, Class 9 on how to draw perpendicular bisector
Justification
We need to prove that AB + AC = BD.
Let perpendicular bisector intersect CD at point R
Thus,
AR is the perpendicular bisector of CD
∴ CR = DR
& ∠ ARC = ∠ ARD = 90°
Now,
In Δ ADR and Δ ACR
AR = AR
∠ ARD = ∠ ARC
DR = CR
∴ Δ ADR ≅ Δ ACR
⇒ AC = AD
Now,
BD = AB + AD
BD = AB + AC
Thus, our construction is justified
(Common)
(From (2))
(From (1))
(SAS Congruency)
(CPCT)
(From (3))

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.