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
In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?
Which congruence criterion do you use in the following?
Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ΔABE ≅ ΔCDB
In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.
D, E, F are the mid-point of the sides BC, CA and AB respectively of ΔABC. Then ΔDEF is congruent to triangle
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD.
Prove that :
(i) ΔABD and ΔECD are congruent.
(ii) AB = CE.
(iii) AB is parallel to EC
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.
A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from the mid-point of BC to AB and AC are equal.
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.
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
