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प्रश्न
Fill in the blank to make the following statement true.
The sum of three altitudes of a triangle is ..... than its perimeter.
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उत्तर
The sum of three altitudes of a triangle is less than its perimeter
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संबंधित प्रश्न
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
- ΔABE ≅ ΔACF
- AB = AC, i.e., ABC is an isosceles triangle.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
Prove that the medians of an equilateral triangle are equal.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
Which of the following statements are true (T) and which are false (F):
Angles opposite to equal sides of a triangle are equal
Which of the following statements are true (T) and which are false (F):
If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
Which of the following statements are true (T) and which are false (F)?
Difference of any two sides of a triangle is equal to the third side.
Fill in the blank to make the following statement true.
In a right triangle the hypotenuse is the .... side.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In the given figure, x + y =
In the given figure, what is z in terms of x and y?
In the given figure, what is y in terms of x?
Which of the following correctly describes the given triangle?
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be ______.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
