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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
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
- OB = OC
- AO bisects ∠A
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
Which of the following statements are true (T) and which are false (F) :
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
Fill the blank in the following so that the following statement is true.
In a ΔABC if ∠A = ∠C , then AB = ......
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)
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than twice the median drawn to the third side.
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Sum of any two sides of a triangle is greater than the third side.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
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?
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
