Advertisements
Advertisements
Question
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that
- ΔABD ≅ ΔBAC
- BD = AC
- ∠ABD = ∠BAC.
Advertisements
Solution
In quadrilateral ABCD, we have
AD = BC and ∠DAB = ∠CBA
i. In ΔABD and ΔBAC,
AD = BC ...[Given]
∠DAB = ∠CBA ...[Given]
AB = BA ...[Common]
∴ ΔABD ≅ ΔBAC ...[By SAS congruency]
ii. Since ΔABD ≅ ΔBAC
BD = AC ...[By Corresponding parts of congruent triangles]
iii. Since ΔABD ≅ ΔBAC
∠ABD = ∠BAC ...[By Corresponding parts of congruent triangles]
APPEARS IN
RELATED QUESTIONS
AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.
In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
Which congruence criterion do you use in the following?
Given: AC = DF
AB = DE
BC = EF
So, ΔABC ≅ ΔDEF
You want to show that ΔART ≅ ΔPEN,
If you have to use SSS criterion, then you need to show
1) AR =
2) RT =
3) AT =
You want to show that ΔART ≅ ΔPEN,
If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
1) RT = and
2) PN =
In the figure, the two triangles are congruent.
The corresponding parts are marked. We can write ΔRAT ≅ ?
If the following pair of the triangle is congruent? state the condition of congruency:
In ΔABC and ΔQRP, AB = QR, ∠B = ∠R and ∠C = P.
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.
If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.
Which of the following is not a criterion for congruence of triangles?
