Question

To construct a triangle, given its base, a base angle and the sum of the other two sides, the property of a/an _________ triangle is used.

• A. scalene
• B. equilateral
• C. right-angled
• D. Isosceles

Answer 1

The correct option is D Isosceles

To construct of a triangle, given its base, a base angle and sum of other two sides, the property of an isoceles triangle is used.

Steps of construction:
1. Draw the base BC and construct ∠ B.
2. With centre B and radius 8 cm (let AB + AC = 8 cm) draw an arc on BX to intersect at D.
3. Join CD and draw a perpendicular bisector of CD to meet BD at A
4.Join AC to get the required triangle ABC.


Now AD = AC [Isosceles Triangle]

Proof :
A lies on the perpendicular bisector of CD
$\therefore$ AC = AD
AB + AC = AB + AD
= BD
= 8 cm.
Hence ABC is the required triangle.