Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given that ABCD is a square, X and Y are points on sides AD and BC respectively such that AY = BX.
We have to prove BY = AX and ∠BAY = ∠ABX
Join B and X, A and Y.
Since, ABCD is a square ⇒ ∠ DAB = ∠CBA =90°
⇒ ∠XAB= ∠YBA=90° .............(1)
Now, consider triangle XAB and YBA
We have
∠XAB=∠YBA=90° ...........[From (1)]
BX=AY [given]
And AB=BA [Common side]
So, by RHS congruence criterion, we have ΔXAB≅ΔYBA
Now, we know that corresponding parts of congruent triangles are equal.
∴ BY=AX and ∠BAY=∠ABX
∴ Hence proved
APPEARS IN
RELATED QUESTIONS
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that
- ΔABD ≅ ΔBAC
- BD = AC
- ∠ABD = ∠BAC.
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.
In Fig. 10.99, AD ⊥ CD and CB ⊥. CD. If AQ = BP and DP = CQ, prove that ∠DAQ = ∠CBP.
In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.
ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:
AB = CE.
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.
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 following figure, OA = OC and AB = BC.
Prove that: ΔAOD≅ ΔCOD
ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2AD.
