Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
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 =
ABCD is a square, X and Yare points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX.
In two triangles ABC and DEF, it is given that ∠A = ∠D, ∠B = ∠E and ∠C =∠F. Are the two triangles necessarily congruent?
ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.
In ∆ABC, AB = AC. Show that the altitude AD is median also.
In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.
Prove that: BD = CD
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.
A point O is taken inside a rhombus ABCD such that its distance from the vertices B and D are equal. Show that AOC is a straight line.
In the following figure, ABC is an equilateral triangle in which QP is parallel to AC. Side AC is produced up to point R so that CR = BP.
Prove that QR bisects PC.
Hint: ( Show that ∆ QBP is equilateral
⇒ BP = PQ, but BP = CR
⇒ PQ = CR ⇒ ∆ QPM ≅ ∆ RCM ).
PQRS is a parallelogram. L and M are points on PQ and SR respectively such that PL = MR.
Show that LM and QS bisect each other.
