Advertisements
Advertisements
Question
l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ΔABC ≅ ΔCDA.
Advertisements
Solution
l || m ...[Given]
AC is a transversal.
So, ∠DAC = ∠ACB ...[Alternate angles]
p || q ...[Given]
AC is a transversal.
So, ∠BAC = ∠ACD ...[Alternate angles]
Now, △ABC and △CDA,
∠ACB = ∠DAC ...[Proved above]
∠BAC = ∠ACD ...[Proved above]
AC = AC ...[Common]
△ABC ≌ △CDA ...[By AAS congruence rule]
APPEARS IN
RELATED QUESTIONS
Which congruence criterion do you use in the following?
Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ΔPQR ≅ ΔXYZ
You want to show that ΔART ≅ ΔPEN,
If it is given that AT = PN and you are to use ASA criterion, you need to have
1) ?
2) ?
In Fig. 10.92, it is given that AB = CD and AD = BC. Prove that ΔADC ≅ ΔCBA.
In two triangles ABC and DEF, it is given that ∠A = ∠D, ∠B = ∠E and ∠C =∠F. Are the two triangles necessarily congruent?
In triangles ABC and CDE, if AC = CE, BC = CD, ∠A = 60°, ∠C = 30° and ∠D = 90°. Are two triangles congruent?
ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.
The perpendicular bisectors of the sides of a triangle ABC meet at I.
Prove that: IA = IB = IC.
In the parallelogram ABCD, the angles A and C are obtuse. Points X and Y are taken on the diagonal BD such that the angles XAD and YCB are right angles.
Prove that: XA = YC.
In the figure, given below, triangle ABC is right-angled at B. ABPQ and ACRS are squares. 
Prove that:
(i) ΔACQ and ΔASB are congruent.
(ii) CQ = BS.
ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2AD.
