Answer:
Part 1)
Part a) Yes, triangle ABC is congruent with triangle DEC by SAS
Part b) No, triangle ABC is not congruent with triangle DCE
Part 2) No, is not enough information
Part 3) Yes, triangle RST is congruent with triangle VUT by ASA
Part 4) Yes, triangle DEF is congruent with triangle DHG by SAS
Step-by-step explanation:
Part 1) we have two cases
Part a) Is triangle ABC and DEC congruent?
Yes, triangle ABC is congruent with triangle DEC by SAS
we know that
The <u><em>Side Angle Side postulate</em></u> ( SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent
In this problem
AC≅DE
BC≅EC
and
∠ACB≅∠DCE ---> by vertical angles
Part b) Is triangle ABC and DCE congruent?
we know that
If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent
In this problem
the corresponding sides are not congruent
because
AB is not congruent with DC
Part 2) we have that
No, is not enough information
If AC≅XZ then the triangles ABC and XYZ will be congruent by SSS
or
If ∠ABC≅∠XYZ then the triangles ABC and XYZ will be congruent by SAS
Part 3) we have that
Yes, triangle RST is congruent with triangle VUT by ASA
we know that
If any two angles and the included side are the same in both triangles, then the triangles are congruent by Angle -Side-Angle (ASA) postulate
In this problem
ST≅UT
∠RST≅∠VUT ----> is a right angle
∠RTS≅∠VTU ---->by vertical angles
so
Two angles and the included side are the same in both triangles
therefore
triangles RST and VUT are congruent by ASA
Part 4) we have that
Yes, triangle DEF is congruent with triangle DHG by SAS
we know that
The <u><em>Side Angle Side postulate</em></u> ( SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent
In this problem
DE≅DH
DF≅DG
and
∠EDF≅∠HDG ---> by vertical angles
