Advertisements
Advertisements
Question
In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
Advertisements
Solution
Given that
∠BAD = ∠EAC
On adding ∠DAC on both sides, we get
∠BAD + ∠DAC = ∠EAC + ∠DAC
⇒ ∠BAC = ∠EAD …(I)
Now, in △ABC and △AED,
AB = AD ...[Given]
AC = AE ...[Given]
∠BAC = ∠EAD ...[By (I)]
∴ △ABC ≌ △ADE ...[By AAS congruence rule]
⇒ BC = DE ...[Corresponding parts of congruent triangles]
APPEARS IN
RELATED QUESTIONS
In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?
Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:
- ΔAPB ≅ ΔAQB
- BP = BQ or B is equidistant from the arms of ∠A.
Which congruence criterion do you use in the following?
Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ΔLMN ≅ ΔGFH
Which congruence criterion do you use in the following?
Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ΔABE ≅ ΔCDB
Explain, why ΔABC ≅ ΔFED.
In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.
In two triangles ABC and DEF, it is given that ∠A = ∠D, ∠B = ∠E and ∠C =∠F. Are the two triangles necessarily congruent?
In the given figure, ABC is an isosceles triangle whose side AC is produced to E. Through C, CD is drawn parallel to BA. The value of x is
D, E, F are the mid-point of the sides BC, CA and AB respectively of ΔABC. Then ΔDEF is congruent to triangle
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:
AB is parallel to EC.
