Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given that, in two right triangles one side and acute angle of one are equal to the corresponding side and angle of the other
We have to prove that the triangles are congruent
Let us consider two right triangles such that
∠B=∠E=90° .................(1)
AB=DE ..................(2)
∠C=∠F ..................(3)
Now observe the two triangles ABC and DEF
∠C=∠F [From (3)]
∠B=∠E [From (4)]
and AB =DE [From (2)]
So, by AAS congruence criterion, we have
ΔABC≅ΔDEF
∴ The two triangles are congruent
Hence proved
APPEARS IN
संबंधित प्रश्न
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.
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
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.
Prove that the medians of an equilateral triangle are equal.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
Which of the following statements are true (T) and which are false (F):
If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
In a ΔABC, if ∠B = ∠C = 45°, which is the longest side?
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)?
Sum of any two sides of a triangle is greater than the third side.
Fill in the blank to make the following statement true.
If two angles of a triangle are unequal, then the smaller angle has the........ side opposite to it.
Write the sum of the angles of an obtuse triangle.
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
In the given figure, if AB ⊥ BC. then x =
In the given figure, what is z in terms of x and y?
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
The angles of a right angled triangle are
Find all the angles of an equilateral triangle.
