Question

Consider the triangles made by two intersecting lines as shown.What additional information is required to prove that ∆TOI ≅∆SOD? ​

Answer 1

Answer:

here is the answer

Step-by-step explanation:

SAS Congruence rule :Two triangle are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.

In △GHJ and △RTS,HJ=TS ( side ) ---(1)

∠GHJ=∠STR ( included angle )--(2)

HG=TR ( side )-----(GIVEN)

∴,△GHJ Congruent to △RTS

Information (1) and (2) required to prove ( SAS ) congruence. 

Answer 2

Given:

Two triangles are made by two intersecting lines

To Prove:

ΔTOI ≅ ΔSOD

Solution:

To prove that ΔTOI ≅ ΔSOD the additional that is required is ∠OTI = ∠ODI

Now, according to the SAS Congruence criteria, two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.

So, In ΔTOI and ΔSOD

OI = OD [sides of the triangle] ..(i)

∠OTI = ∠ODI  [included angles of the triangle] ..(ii)

OT = DI [sides of the triangle so they are equal]

∴ ΔTOI ≅ ΔSOD using (i) and (ii) by SAS Congruence criteria.