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प्रश्न
Fill the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
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उत्तर
In an equilateral triangle all angles are equal Reason: Since all sides are equal in a equilateral triangle, the angles opposite to equal sides will be equal
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संबंधित प्रश्न
Find the measure of each exterior angle of an equilateral triangle.
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
Prove that each angle of an equilateral triangle is 60°.
Which of the following statements are true (T) and which are false (F):
The measure of each angle of an equilateral triangle is 60°
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.
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.
Fill in the blank to make the following statement true.
The sum of three altitudes of a triangle is ..... than its perimeter.
Fill in the blank to make the following statement true.
Difference 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.
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?
In the given figure, the value of x is ______.
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC = ______.
M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC. Is it true to say that perimeter of the triangle is greater than 2 AM? Give reason for your answer.
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].
