Question

Fill In The Blanks

Given: RT¯¯¯¯¯¯¯≅ZT¯¯¯¯¯¯¯
and ST¯¯¯¯¯¯¯≅XT¯¯¯¯¯¯¯¯
Prove: RS¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯

(4 points)
The diagram shows that <RTS ≅
<XTZ due to (fill)
. We are also know that RT¯¯¯¯¯¯¯≅ZT¯¯¯¯¯¯¯
and ST¯¯¯¯¯¯¯≅XT¯¯¯¯¯¯¯¯
because (fill)
. Because of these things, we know that △RTS≅ZTX
by (fill)
. Finally we can prove RS¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
by (fill)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The diagram shows that <RTS ≅ <XTZ due to the angle-side-angle (ASA) congruence criterion. We also know that RT¯¯¯¯¯¯¯≅ZT¯¯¯¯¯¯¯ and ST¯¯¯¯¯¯¯≅XT¯¯¯¯¯¯¯¯ because of the given information. Because of these things, we know that △RTS≅△ZTX by the side-angle-side (SAS) congruence criterion. Finally, we can prove RS¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯ by the corresponding parts of congruent triangles (CPCTC) theorem.