Complete the two-column proof
Given: triangle SVX is congruent to triangle UTX and Line SV is || to line TU
Prove: VUTS is a parallelogram
Image: It's a parallelogram, with one line going from corner S to corner U and a line going from corner T to corner V. X being the center. If you draw this out corner S is at the Top Left-Hand corner with V being at the Top Right-hand corner. T being at the bottom left-hand corner and U at the bottom right-hand corner. And again X being in the center. That's has much as I can possibly describe this picture.
Statements:
1. Triangle SVX is congruent to triangle UTX
2. __________
3.__________
4. VUTS is a parallelogram
Reasons:
1. Given
2. Given
3. _________
4. _________
I already have statement 2 which is Line SV || line TU. However that's as far as I've gotten. Can someone please help me understand this. Thank you and God Bless!
Note: If you need anymore details let me know and I'll see if i can describe what you may need.
Statements:
1. Triangle SVX is congruent to triangle UTX
2. Line ST is parallel to line TU.
3. Line ST is congruent to line TU.
4. VUTS is a parallelogram.
Reasons:
1. Given
2. Given
3. Corresponding parts of a congruent triangle.
4. Definition of a parallelogram.
Also here is the rest of the quiz.
1. A (Always true)
2. A (128.6 degrees)
3. B (21)
4. C (Octagon)
5. C (135 degrees)
6. I'm not 100% sure so sorry you will have to do it yourself :(
7. The diagram has four sides, two pairs of equivalent angles, and two pairs of equivalent sides. This is proven by the definition of a parallelogram.
Hope this helps also 1-5 are 100% correct
The rest are my guess.
the answer to number to is SV is congruent to TU
6 is 96 I think
To complete the two-column proof, let's use the given information "Line SV is parallel to line TU" and the congruence of triangles SVX and UTX.
Statements:
1. Triangle SVX is congruent to triangle UTX (Given)
2. Line SV is parallel to line TU (Given)
3. Angle SVX is congruent to angle UTX (Corresponding parts of congruent triangles are congruent)
4. Angle VXS is congruent to angle UTX (Corresponding angles in congruent triangles are congruent)
5. Angle VXS is congruent to angle VUS (Alternate interior angles formed by parallel lines)
6. Angle VUS is congruent to angle VUT (Vertical angles)
7. Angle VUT is congruent to angle TXU (Corresponding angles in congruent triangles are congruent)
8. Angle VUT is congruent to angle VTS (Alternate interior angles formed by parallel lines)
9. Opposite angles VUS and VTS are congruent (Opposite angles in a parallelogram)
10. Opposite sides VS and UT are congruent (Corresponding sides in congruent triangles are congruent)
11. Opposite sides VT and US are congruent (Corresponding sides in congruent triangles are congruent)
12. Opposite sides VU and ST are congruent (Corresponding sides in congruent triangles are congruent)
13. Opposite sides VS and UT are parallel (Given: SV || TU)
14. Opposite sides VT and US are parallel (Alternate interior angles formed by parallel lines)
15. Opposite sides VU and ST are parallel (Given: SV || TU)
16. VUTS is a parallelogram (Definition of a parallelogram)
Reasons:
1. Given
2. Given
3. Corresponding parts of congruent triangles are congruent (CPCTC)
4. Corresponding angles in congruent triangles are congruent (CPCTC)
5. Alternate interior angles formed by parallel lines
6. Vertical angles
7. Corresponding angles in congruent triangles are congruent (CPCTC)
8. Alternate interior angles formed by parallel lines
9. Opposite angles in a parallelogram are congruent
10. Corresponding sides in congruent triangles are congruent (CPCTC)
11. Corresponding sides in congruent triangles are congruent (CPCTC)
12. Corresponding sides in congruent triangles are congruent (CPCTC)
13. Given: SV || TU
14. Alternate interior angles formed by parallel lines
15. Given: SV || TU
16. Definition of a parallelogram