1. Unit 2 – Similarity, Congruence, and Proofs
Review Quiz #10
Proving Theorems about
Parallelograms

2. No, because both pairs of opposite sides are not parallel.
Question 1
Determine whether these four vertices form a parallelogram: A (–3, 0), B (6, 0), C (1, 1), D (–2, –2).
No, because both pairs of opposite sides are not parallel.

3. Yes, because both pairs of opposite sides are parallel.
Question 2
Determine whether these four vertices form a parallelogram: S (–7, 3), T (–1, 3), U (–2, 1), V (–8, 1).
Yes, because both pairs of opposite sides are parallel.

4. Question 3
Classify a quadrilateral as precisely as possible given four vertices: P (–6, –3), Q (–3, –7), R (–7, –10),
S (–10, –6).
Square

5. Question 4
Classify a quadrilateral as precisely as possible given four vertices: D (–5, 2), E (–2, –3), F (8, 3), G (5, 8).
Rectangle

6. The diagonals intersect at right angles.
Question 5
What is always true about rhombuses?
The diagonals intersect at right angles.

7. Question 6
Decide whether each statement is true or false about the properties of parallelograms.
Opposite angles are congruent.
TRUE
The diagonals bisect each other.
TRUE
The diagonals are perpendicular.
FALSE
Consecutive angles are supplementary.
TRUE

8. Yes, because the diagonals bisect each other.
Question 7
Determine whether the four vertices form a parallelogram: P (3, 3), Q (7, 4), R (5, 2), S (1, 1).
Yes, because the diagonals bisect each other.

9. No, because the opposite sides are not parallel.
Question 8
Determine whether the four vertices form a parallelogram: D (0, 4), E (3, 5), F (2, 2), G (–1, 2).
No, because the opposite sides are not parallel.

10. Find the values of x and y if quadrilateral ABCD is a parallelogram.
Question 9
Find the values of x and y if quadrilateral ABCD is a parallelogram.
x = 19, y = 17

11. Question 10
Find the values of x and y if quadrilateral ABCD is a parallelogram.
x = 13, y = 22

12. Question 11
If the diagonals of a given quadrilateral are perpendicular, how could the quadrilateral
be classified?
Rhombus, Square, Kite

13. Rectangle, Isosceles Trapezoid, Square
Question 12
If the diagonals of a given quadrilateral are congruent, how could the quadrilateral be classified?
Rectangle, Isosceles Trapezoid, Square

14. Question 13
Classify a quadrilateral as precisely as possible given four vertices: E (0, –1), F (3, –5), G (–2, –5),
and H (–5, –1).
rhombus

15. Question 14
Classify a quadrilateral as precisely as possible given four vertices: A (1, 1), B (6, 6), C (11, 1),
and D (6, –4).
square

16. Question 15
Classify a quadrilateral as precisely as possible given four vertices: A (3, –5), B (3, 3), C (9, 1), and D (9, –3).
isosceles trapezoid