Question

Please help asap no trolls!

Answer 1

`D. These\ triangles\ cannot\ be\ proven\ congruent`

Explanation:

`We\ are\ given:\\TU=SQ\\TP=PQ\\\angle TPU= \angle SPQ [Vertically\ Opposite\ Angles\ Are\ Equal]\\Hence,\\As\ we\ are\ given,\ 2\ sides\ and\ 1\ angle\ of\ each\ triangle\ correspond,\ we\\ could\ use\ the\ SAS\ Congruency Rule.\\But:\\`

As SAS Congruency Rule tells us that 'Two triangles are congruent only if two sides and an included angle of one triangle corresponds to two sides and an included angle of the other' .

Here,

As ∠TPU and ∠SPQ are NOT the included angle of ΔTUP and ΔSPQ respectively, the two triangles cannot be proven congruent through SAS Congruency.

Note: We also cannot apply SSA congruency as SSA congruency doesnt exist.