Advertisements
Advertisements
प्रश्न
In the following figure, D and E are points on side BC of a ∆ABC such that BD = CE and AD = AE. Show that ∆ABD ≅ ∆ACE.
Advertisements
उत्तर
Given: D and E are the points on side BC of a ∆ABC such that BD = CE and AD = AE.
To show: ∆ABD ≅ ∆ACE
Proof: We have, AD = AE ...[Given]
⇒ ∠ADE = ∠AED ...(i) [Since, angles opposite to equal sides are equal]
We have, ∠ADB + ∠ADE = 180° ...[Linear pair axiom]
⇒ ∠ADB = 180° – ∠ADE
= 180° – ∠AED ...[From equation (i)]
In ∆ABD and ∆ACE,
∠ADB = ∠AEC ...[∵ ∠AEC + ∠AED = 180°, linear pair axiom]
BD = CE ...[Given]
And AD = AE ...[Given]
∴ ∆ABD ≅ ∆ACE ...[By SAS congruence rule]
APPEARS IN
संबंधित प्रश्न
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
The vertical angle of an isosceles triangle is 100°. Find its base angles.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
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):
The measure of each angle of an equilateral triangle is 60°
Which of the following statements are true (T) and which are false (F):
The two altitudes corresponding to two equal sides of a triangle need not be equal.
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.
Fill in the blank to make the following statement true.
The sum of three altitudes of a triangle is ..... than its perimeter.
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
In the given figure, what is z in terms of x and y?
In the given figure, the value of x is ______.
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 = ______.
It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
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.
