In a square ABCD, the diagonals meet at point O. The ∆AOB is
(a) isosceles right triangle
(b) equilateral triangle
(c) isosceles triangle but not right triangle
(d) scalene right triangle.
Solution:
Given, ABCD is a square.
The diagonals meet at point O.
We have to find the type of triangle AOB.
A square is a two-dimensional plane figure with four equal sides.
There are only two diagonals of the square and they bisect each other at right angles.
In the square ABCD,
The sides AB, BC, CD and AD are equal
AB = BC = CD = AD
The diagonals AC and BD bisect each other.
AO = OC = BO = OD
Also, ∠A = ∠B = ∠C = ∠D = 90°
Considering triangle AOB,
We know, AO = OB
Two sides of the triangle are equal.
Since the diagonal bisect each other,
∠BAO = ∠ABO = 45°
Also, ∠AOB = 90°
Since the two sides of a triangle AOB are equal and one of its angles is a right angle, we can conclude that AOB is a right-angled isosceles triangle.
Therefore, AOB is a right-angled isosceles triangle.
✦ Try This: In a rhombus PQRS, the diagonals meet at point O. The ∆POQ is (a) isosceles right triangle, (b) equilateral triangle, (c) isosceles triangle but not right triangle, (d) scalene right triangle.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 5
In a square ABCD, the diagonals meet at point O. The ∆AOB is, (a) isosceles right triangle, (b) equilateral triangle, (c) isosceles triangle but not right triangle, (d) scalene right triangle
Summary:
In a square ABCD, the diagonals meet at point O. The ∆AOB is isosceles right triangle
☛ Related Questions: