2.Write a flowchart
Given: STV congruent TVU,STU congruent UVS
Prove: SVT congruent UT
To create a flowchart for the given proof, we can use the following steps and geometric properties:
Step 1: Start
Step 2: Draw triangle STV
Step 3: Draw triangle TVU
Step 4: Draw triangle STU
Step 5: Draw triangle UVS
Step 6: Given: STV congruent TVU
Step 7: Draw congruent markings (△ symbol) on STV and TVU
Step 8: Given: STU congruent UVS
Step 9: Draw congruent markings (△ symbol) on STU and UVS
Step 10: Draw line SV and line UT
Step 11: Given: STV congruent TVU, STU congruent UVS
Step 12: Write the statement "STV ≅ TVU" next to the congruent markings on triangle STV and TVU (inside the flowchart)
Step 13: Write the statement "STU ≅ UVS" next to the congruent markings on triangle STU and UVS (inside the flowchart)
Step 14: Write the statement "Line SV ≅ Line UT" next to line SV and UT (inside the flowchart)
Step 15: Write the statement "Prove: SVT ≅ UT" (inside the flowchart)
Step 16: Draw a conclusion box and write "SVT ≅ UT" inside it.
Step 17: End
Here is the flowchart for the given proof:
```
Start
|
| [Step 2: Draw triangle STV]
|
|.
| [Step 3: Draw triangle TVU]
|
|.
| [Step 4: Draw triangle STU]
|
|.
| [Step 5: Draw triangle UVS]
|
|.
| [Step 6: Given: STV congruent TVU]
|
| [Step 7: Draw congruent markings on STV and TVU]
|
| [Step 8: Given: STU congruent UVS]
|
| [Step 9: Draw congruent markings on STU and UVS]
|
| [Step 10: Draw line SV and line UT]
|
| [Step 11: Given: STV congruent TVU, STU congruent UVS]
|
| [Step 12: STV ≅ TVU; STU ≅ UVS]
|
| [Step 13: Line SV ≅ Line UT]
|
| [Step 14: Prove: SVT ≅ UT]
|
| [Step 15: Conclusion: SVT ≅ UT]
|
|.
|
| [Step 16: End]
|
End
```
This flowchart represents the logical steps and geometric properties involved in proving that STV and TVU are congruent, STU and UVS are congruent, and SVT and UT are congruent.