Advertisements
Advertisements
प्रश्न
Prove that the hypotenuse is the longest side in a right-angled triangle.
Advertisements
उत्तर
Let us consider a right angled triangle ABC, right angle at B.
In ΔABC
∠A + ∠B +∠C = 180° ...(angle sum property of a triangle)
∠A + 90° + ∠C = 180°
∠A +∠C = 90°
Hence, the other two angles have to be acute (i.e. less than 90°).
∴ ∠B is the largest angle in ΔABC.
⇒ ∠B > ∠A and ∠B > ∠C
⇒ AC > BC and AC > AB
[In ant triangle, the side opposite to the larger (greater) angle is longer]
So, Ac is the largest side in ΔABC.
But AC is the hypotenuse of ΔABC. Therefore, hypotenuse is the longest side in a right angled triangle.
संबंधित प्रश्न
In a huge park people are concentrated at three points (see the given figure):
A: where there are different slides and swings for children,
B: near which a man-made lake is situated,
C: which is near to a large parking and exit.
Where should an ice-cream parlour be set up so that maximum number of persons can approach it?
(Hint: The parlor should be equidistant from A, B and C)
How had the position of women improved in our country since independence ? Explain with examples.
In a triangle PQR; QR = PR and ∠P = 36o. Which is the largest side of the triangle?
If two sides of a triangle are 8 cm and 13 cm, then the length of the third side is between a cm and b cm. Find the values of a and b such that a is less than b.
For any quadrilateral, prove that its perimeter is greater than the sum of its diagonals.
In ABC, P, Q and R are points on AB, BC and AC respectively. Prove that AB + BC + AC > PQ + QR + PR.
In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PQ > PS
In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PR > PS
In ΔPQR is a triangle and S is any point in its interior. Prove that SQ + SR < PQ + PR.
In ΔABC, AE is the bisector of ∠BAC. D is a point on AC such that AB = AD. Prove that BE = DE and ∠ABD > ∠C.
