Question

questions is in the figure answer please answer and do right iif u do it correctly or nicely I will give u brainlist so please help mee please I need your help plz it's urgent don't spam please answer please guys class 7th sub mathematics please​

Answer 1

i) Yes, △BAC ≅ △DAC.

As, i) ∠BAC = ∠DAS (Ray AZ bisects ∠DAB – given)

ii) AC = AC (Common)

iii) ∠ACB = ∠ACD (Ray AZ bisects ∠DCB – given)

So, by ASA congruence criterion, both the given triangles are congruent.

ii) Yes, as △BAC ≅ △DAC, by corresponding parts of congruent triangles, CD ≅ CB.

Some basic fundamentals:-

• Use ASA only when a side is in between two given equal angles.
• And similarly SAS when an angle is in between two equal sides.
• You can also use AAS congruence criteria to prove to triangles as congruent.

Congruent: having similar properties.

Answer 2

Step-by-step explanation:

Given:-

see the above attachment

To find:-

i) ∆ BAC ≅ ∆ DAC

ii) CD = CB

Solution:-

From the above figure:

Ray AZ is the bisector of angle DAB and angle DCB

From ∆BAC and ∆DAC

angle BCA = angle DCA

(Ray AZ is the bisector of angle DAB and angle DCB)

angle BAC = angle DAC

(Ray AZ is the bisector of angle DAB and angle DCB)

and

AZ = AZ ( Common side)

∆ BAC ≅ ∆ DAC by SAS property

and we have ∆ BAC ≅ ∆ DAC so

CD = CB

(Congruent parts in the Congruent triangles are equal).

Hence, Proved.

Used formulae:-

SAS Property:-

• In two triangles ,The two angles and the included side in a first triangle are equal to the two angles and the included side of the second triangle respectively then the two triangles are congruent and this property is called Angle - Side - Angle Property.

• Congruent parts in the congruent triangles are equal.