    Question

# Pallav got following question in his exam: Given the base angles, say ∠ B and ∠ C and BC + CA + AB, construct triangle ABC. He followed the following steps for the construction. 1. Draw a line segment, say XY equal to BC + CA + AB. 2. Make ∠ LXY equal to ∠ B and ∠ MYX equal to ∠ C. 3. Bisect ∠ LXY and ∠ MYX. Let these bisectors intersect at a point A 4. Draw perpendicular bisectors PQ of AX and RS of AY. 5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC

A

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B True Yes, he has followed correct procedure. 1. Draw a line segment, say XY equal to BC + CA + AB. 2. Make angles ∠ LXY equal to ∠B and ∠ MYX equal to ∠C. 3. Bisect ∠LXY and ∠MYX. Let these bisectors intersect at a point A 4. Draw perpendicular bisectors PQ of AX and RS of AY. 5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC Then ABC is the required triangle. For the justification of the construction, you observe that B lies on the perpendicular bisector PQ of AX. Therefore, XB = AB and similarly, CY = AC. This gives BC + CA + AB = BC + XB + CY = XY. Again ∠BAX =∠ AXB (As in △ AXB, AB = XB) and ∠ABC = ∠BAX + ∠AXB = 2 ∠AXB = ∠LXY [Using exterior angles property] Similarly, ∠ACB = ∠MYX as required.  Suggest Corrections  1      Related Videos   Let's Build Triangles
MATHEMATICS
Watch in App  Explore more