Question

2. If OA=OB and OD=OC. Show that AODABOC.​

Answer 1

Step-by-step explanation:

Given,

OA=OB

OD=OC

angleAOD=angleBOC

To Prove,

∆AOD is congruent to ∆BOC

Proof,

OA=OB [Given]

angleAOD=angleBOC [Given]

OD=OC[Given]

So According to ASA congruence rule

∆AOD is congruent to ∆BOC.

Hope it helps.(•‿•)

Answer 2

$\huge\sf\blue{Question}$

If OA = OB and OD = OC. Show that ▲AOD is congruent to ▲BOC

$\huge\sf\red{Answer}$

To prove :-

▲ AOD is congruent to ▲ BOC

$\sf\red{Given:-}$

OA = OB

OD = OC

$\sf\red{Proof:-}$

OA = OB (given)

Angle 1 = Angle 2 (Vertically opposite angles)

OD = OC (given)

•°• △AOD.⩭ △BOC

By S.A.S

Hence proved.

▬▬▬▬▬▬▬▬▬

Additional

Information

Conditions for Congruency of Triangles:-

▪S.A.S

If two sides of one triangle are equal to the other two sides of the other triangle and one angle is equal to the other angle of the other triangle then the triangle is proved congruent by S.A.S

▪A.S.A

If two angles of one triangle are equal to the two angles of the other triangle and one side is equal to the other side of the other triangle then the triangle is proved congruent by A.S.A

▪A.A.S

If two angles of one triangle are equal to the two angles of the other triangle and one side is equal to the other then the triangle is proved congruent by A.A.S

▪S.S.S

If all the sides of a triangle are equal to the other triangle's sides then the triangle is proved congruent by S.S.S

▪R.H.S

If the hypotenuse and one side is equal to the hypotenuse and a side of the other triangle then the triangle is proved congruent by R.H.S