Question

Name the postulate or theorem you can use to prove

SSS Postulate

ASA Postulate

AAS Theorem

SAS Postulate

Answer 1

AAS

A for <SUR and <TVR

A for <SRU and <TRV

S for SU and TV

Answer 2

Answer: AAS Theorem

Explanation:

In the given figure , we have

`\triangle{STU}\cong\triangle{TSV}`

By CPCTC [Congruent parts of congruent triangles are congruent], we have

`\angle{SUR}\cong\angle{TVR}` (1)

`\overline{SU}\cong\overline{TV}` (2)

Now in
`\triangle{SUR}\text{ and }\triangle{TVR}`, we have

`\angle{SUR}\cong\angle{TVR}` (From 1)

`\overline{SU}\cong\overline{TV}` (From 2)

`\angle{SRU}\cong\angle{TRV}` (Vertical angles)

Therefore by AAS theorem of congruence , we have

`\triangle{SUR}\cong\triangle{TVR}`

• AAS theorem of congruence says that if two angles and a non-included side of a triangle are congruent to the corresponding parts of other triangle then the triangles are said to be congruent.