    Question

# A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows: 1. Draw a line segment, say XY equal to AB + BC + AC 2. Make angles LXY equal to ∠B and angle MYX equal to ∠C 3. Bisect ∠LXY and ∠MXY. Let these bisectors intersect each other at A. 4. Draw perpendicular bisectors DE of AX and FG of AY 5. Let DE intersect XY at B and FG intersect XY at C. Join AB and AC. 6. The triangle ABC is thus formed. How many isosceles triangles are there in this figure? A

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

2

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

4

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

## The correct option is C 2 If we take △ XBQ and △ ABQ, we have XQ = AQ and ∠ BQX = ∠ AQB = 90° (Since DE is the perpendicular bisector of AX) BQ = BQ (common side) △ XBQ ≅ △ ABQ (By SAS congruency) XB = AB (By C.P.C.T.) Similarly, taking △ ACR and △ YCR, we have AR = YR and ∠ ARC = ∠ YRC = 90° (Since FG is the perpendicular bisector AY) CR = CR (common side) △ ACR ≅ △ YCR (By SAS Congruency) AC = CY (By C.P.C.T.) Hence the triangle ABX and triangle ACY are isosceles triangles. .   Suggest Corrections  0      Related Videos   Criteria for Congruency
MATHEMATICS
Watch in App  Explore more