1. Quadrilateral ABCD has vertices A(6,0), B(3,9), C(-3,7) and D(0,-2). Prove that ABCD is a rectangle.

2. W

X

Z

Y

Given: WX ⊥ XYZY ⊥ XYm W = m Z

Prove: WX = ZY

3. Complete the given partial proof by providing the missing statements and/or reasons.

U

P Q R

V

S T34 2

1

Given: PQRSTR is the midpoint of QS 1 ≅ 2

Prove: U ≅ V

STATEMENTS REASONS

1. PQRST, R is the midpoint of QS, 1 ≅ 22. QR ≅ RS

3. 1 supplementary to 3 2 supplementary to 4

4.

5. URQ ≅ SRV

6.

7. U ≅ V

1. Given

2.

3.

4. If 2 angles are supp. to the same angle or congruent angles, they are congruent to each other.

5.

6. a.s.a. ≅ a.s.a.

7.

ANSWERS1. Quadrilateral ABCD has vertices A(6,0), B(3,9), C(-3,7) and D(0,-2). Prove that ABCD is a rectangle.

Use slope formula: y2 - y

1

x2 - x

1

AB = = =

BC = = =

9 - 03 - 6

9-3

-31

7 - 9-3 - 3

-2-6

13

CD = = =

AD = = =

2 - 70 - (-3)

-93

-31

-2 - 00 - 6

-2-6

13

2. W

X

Z

Y

Given: WX ⊥ XYZY ⊥ XYm W = m Z

Prove: WX = ZY

STATEMENTS REASONS

1. WX ⊥ XY, ZY ⊥ XY, m W = Z2. WX = ZY3. WXY and ZYX are right angles4. WXY = ZYX5. XY = XY6. ∆ZYX ≅ ∆WXY7. m W = m Z

8. WX = ZY

1. Given2. Assumption3. Perpendicular lines form right angles4. All right angles are equal5. Reflexive property6. s.a.s. ≅ s.a.s.7. Corresponding parts of congruent triangles are congruent8. Contradiction (steps 1, 7)

3. Complete the given partial proof by providing the missing statements and/or reasons.

U

P Q R

V

S T34 2

1

Given: PQRSTR is the midpoint of QS 1 ≅ 2

Prove: U ≅ V

STATEMENTS REASONS

1. PQRST, R is the midpoint of QS, 1 ≅ 22. QR ≅ RS

3. 1 supplementary to 3 2 supplementary to 4

4. 3 ≅ 4

5. URQ ≅ SRV

6. ∆URQ ≅ ∆SRV

7. U ≅ V

1. Given

2. A midpoint divides a line segment into two congruent line segments

3. Two adjacent angles on a straight line are supplementary

4. If 2 angles are supp. to the same angle or congruent angles, they are congruent to each other.

5. Vertical angles are congruent

6. a.s.a. ≅ a.s.a.

7. Corresponding parts of congruent triangles are congruent.