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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.
Find the measure of each exterior angle of an equilateral triangle.
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.
Fill the blank in the following so that the following statement is true.
Sides opposite to equal angles of a triangle are ......
Fill the blank in the following so that the following statement is true.
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……
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.
Fill in the blank to make the following statement true.
The sum of any two sides of a triangle is .... than the third side.
Fill in the blank to make the following statement true.
If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
Write the sum of the angles of an obtuse triangle.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In the given figure, if AB ⊥ BC. then x =
In the given figure, what is y in terms of x?
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
In ∆PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is the longest? Give reason for your answer.
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
Find all the angles of an equilateral triangle.
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
What is the defect in the above arguments?
[Hint: Recall how ∠B = ∠C is proved when AB = 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.
