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प्रश्न
Fill in the blank to make the following statement true.
The sum of any two sides of a triangle is .... than the third side.
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उत्तर
The sum of any two sides of a triangle is greater than the third side.
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संबंधित प्रश्न
In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
Find the measure of each exterior angle of an equilateral 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.
In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
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.
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.
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.
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
Fill the blank in the following so that the following statement is true.
Sides opposite to equal angles of a triangle are ......
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.
Which of the following statements are true (T) and which are false (F)?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.
In the given figure, what is z in terms of x and y?
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
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].
