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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.
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.
In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
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.
If the angles A, B and C of ΔABC satisfy the relation B − A = C − B, then find the measure of ∠B.
In the given figure, x + y =
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
