Geometry Proof-- Need Help

[Bullet_Dodger]

I know this is kind of ridiculous, but I am weeks behind my work due to an illness, and I have no idea what I'm doing. Any help is appreciated. Thanks.

1. Given quadrilateral PQRS with vertices P (-2,3) Q (1,0) R (7,6) and S (0,5) prove that PQRS is a trapezoid.

2. Prove, using coordinate geometry, that the diagonals of isosceles trapezoid FISH with vertices F (2a, b) I (5a, b) S (7a,0) and H (0,0) are congruent

4. Given: Parallelogram ABCD
Line CE is perpendicular to Line AB
Line CF is perpendicular to Line AD
Prove: Triangle DCF ~ Triangle BCE

5. Given: Triangle ABC is isosceles with base Line AC
Line BD bisects angle ABC
Prove: Triangle ADB is congruent to Triangle CDB

6. Given: R is the midpoint of Line QS
QS bisects Line PT
Prove: Line PQ is congruent to Line TS

7. Given: Triangle BAT, line CBTD and Line AB are perpendicular to CD

Write an indirect proof to show that line AT is not perpendicular to Line CD

[TomCollins]

1. Given quadrilateral PQRS with vertices P (-2,3) Q (1,0) R (7,6) and S (0,5) prove that PQRS is a trapezoid.
Trapezoids have two parallel edges. Draw it out, figure out which ones are parallel, then prove it with math

[Bullet_Dodger]

[ QUOTE ]
1. Given quadrilateral PQRS with vertices P (-2,3) Q (1,0) R (7,6) and S (0,5) prove that PQRS is a trapezoid.
Trapezoids have two parallel edges. Draw it out, figure out which ones are parallel, then prove it with math

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Ill try that, thanks

[Nottom]

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2. Prove, using coordinate geometry, that the diagonals of isosceles trapezoid FISH with vertices F (2a, b) I (5a, b) S (7a,0) and H (0,0) are congruent

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Find the 2 non-parallel sides and compute their lengths.

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4. Given: Parallelogram ABCD
Line CE is perpendicular to Line AB
Line CF is perpendicular to Line AD
Prove: Triangle DCF ~ Triangle BCE

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I'm not sure what the picture looks like here, but I'd imagine you will be using ASA to prove congruence.

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5. Given: Triangle ABC is isosceles with base Line AC
Line BD bisects angle ABC
Prove: Triangle ADB is congruent to Triangle CDB

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Use AAS

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6. Given: R is the midpoint of Line QS
QS bisects Line PT
Prove: Line PQ is congruent to Line TS

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I assume PT passes through point R.
If so you can use SAS to show triangles QRP and SRT are congruent.


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7. Given: Triangle BAT, line CBTD and Line AB are perpendicular to CD

Write an indirect proof to show that line AT is not perpendicular to Line CD

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I can't really picture this. But I think you just assume AT is perp but then angle BAT = 0 which isn't true since ABT is a triangle. Thus the assumption can't be true.