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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.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Fill the blank in the following so that the following statement is true.
In a ΔABC if ∠A = ∠C , then AB = ......
Fill the blank in the following so that the following statement is true.
In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC
(iii) OA + OB + OC >` 1/2`(AB + BC + CA)
Write the sum of the angles of an obtuse triangle.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
In a triangle ABC, D is the mid-point of side AC such that BD = `1/2` AC. Show that ∠ABC is a right angle.
