Advertisements
Advertisements
प्रश्न
In quadrilateral ABCD, AD = BC and BD = CA.
Prove that:
(i) ∠ADB = ∠BCA
(ii) ∠DAB = ∠CBA
Advertisements
उत्तर
Given: In quadrilateral ABCD, AD = BC and BD = AC.
To Prove:
(i) ∠ADB = ∠BCA
(ii) ∠DAB = ∠CBA
Proof:
In ΔABD and ΔBAC,
AD = BC ....(given)
BD = CA ....(given)
AB = AB ....(common)
∴ ΔABD ≅ ΔBAC ....(by SSS congruence criterion)
`{:(∠"ADB" = ∠"BCA"), (∠"DAB" = ∠"CBA"):}} ...("c.p.c.t.")`
APPEARS IN
संबंधित प्रश्न
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.
Which of the following statements are true (T) and which are false (F):
Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.
In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.
The following figure shows a circle with center O.
If OP is perpendicular to AB, prove that AP = BP.
In the given figure, AB = DB and Ac = DC.
If ∠ ABD = 58o,
∠ DBC = (2x - 4)o,
∠ ACB = y + 15o and
∠ DCB = 63o ; find the values of x and y.
In the given figure: AB//FD, AC//GE and BD = CE;
prove that:
- BG = DF
- CF = EG
In the following figure, BL = CM.
Prove that AD is a median of triangle ABC.
In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.
Prove that : ED = EF
Which of the following is not a criterion for congruence of triangles?
ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE.
