Download Name: ______ Date: _________ Period: ____________ Unit 2

Name: _____________________________
Date: ____________
Period: ________________
Unit 2: Quadrilaterals
Geometry Homework Packet
Angle Relationships in Parallel Lines Cut by a Transversal
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Transversal—line that intersects with two parallel lines
__________________—two angles that are directly across from each other; example:  1 and  4
o ALWAYS congruent to each other (even if lines are not parallel)
o Form an “X”
Corresponding angles—________________________________________________; example:  2 and  6
o Congruent to each other when lines are parallel
Alternate Interior Angles— two angles that are inside the parallel lines and on opposite sides of the transversal;
example: ___________________
o Congruent to each other when lines are parallel
o Form a “Z”
_________________________—two angles that are inside the parallel lines and on the same side of the transversal;
example;  3 and  5
o Supplementary when lines are parallel
Supplementary Angles—two angles that add up to ______________
o Example:  3 and  5,  5 and  8
Practice Problems:
1. In the accompanying figure, what is one pair of alternate interior angles?
(A)  1 and  2
(B)  4 and  5
(C)  4 and  6
(D)  6 and  8
2. In the accompanying diagram, lines a and b are parallel, and lines c and d are transversals.
Which angle is congruent to  8?
(A)  6
(C)  3
(B)  5
(D)  4
3. Two parallel roads, Elm Street and Oak Street, are crossed by a third, Walnut Street, as shown in the accompanying
diagram. Find the number of degrees in the acute angle formed by the intersection of Walnut Street and Elm Street.
4. The diagram below illustrates the construction of PS parallel to RQ through point P. Which statement justifies this
construction. Explain why.
(A) m  1 = m  2
(C) PR  RQ
(B) m  1 = m  3
(D) PS  RQ
Interior and Exterior Angles in a Polygon
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___________ polygon—polygon with all angles and all sides congruent
Sum of interior angles of a polygon = _______________, n is the number of sides
o
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Interior angle of a regular polygon =
(n  2)  180
n
o Example: sum of interior angles of a pentagon = (5 – 2) × 180 = 540 degrees
o Example: interior angle of a regular pentagon = 540 / 5 = 108 degrees
Sum of exterior angles of a polygon = ______ for ANY polygon, no matter how many sides it has
o
Exterior angle of a regular polygon =
360
n
Practice Problems:
5. What is the sum of the measures of the interior angles of an octagon?
6. What is the sum, in degrees, of the measures of the exterior angles of a pentagon?
7. The measures of five of the interior angles of a hexagon are 150°, 100°, 80°, 165°, and 150°. What is the measure of
the sixth interior angle?
8. What is the measure of an interior angle of a regular octagon?
9. What is the measure, in degrees, of each exterior angle of a regular hexagon?
10. A stop sign in the shape of a regular octagon is resting on a brick wall, as shown in the accompanying diagram. What
is the measure of angle x?
Parallelograms
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Parallelogram—quadrilateral with opposite sides parallel
o Opposite sides are _______________
o Opposite sides are _______________
o __________________ are congruent
o Diagonals ______________________
Practice Problems:
11. Which statement is not always true about a parallelogram?
(A) The diagonals are congruent.
(B) The opposite sides are congruent.
(C) The opposite angles are congruent.
(D) The opposite sides are parallel
12. In the accompanying diagram of parallelogram ABCD, diagonals AC and BD intersect at E, AE = 3x – 4, and
AC =6 x + 12. What is the value of x?
13. In the accompanying diagram of parallelogram ABCD, diagonals AC and BD intersect at E, BE 
ED  x  10. What is the value of x?
2
x, and
3
14. In the accompanying diagram of parallelogram ABCD, m∠A = 2x + 10 and m∠B = 3x. Find the number of degrees in
m∠B.
Rhombuses, Rectangles, and Squares
 ________________—parallelogram with all four sides congruent
o All four sides are congruent
o Diagonals are perpendicular to each other
 Rectangle—parallelogram with four ___________________
o Diagonals are ________________
 ______________—parallelogram with four right angles and all four sides congruent (combination of rhombus and
rectangle)
o Four right angles
o Four sides congruent
o Diagonals are ______________________________
Practice Problems:
15. Which quadrilateral must have diagonals that are congruent and perpendicular?
(A) rhombus
(C) trapezoid
(B) square
(D) parallelogram
16. In rectangle ABCD, AC = 3x + 15 and BD = 4x – 5. Find the length of AC .
17. In the accompanying diagram of rectangle ABCD, m  BAC = 3x + 4 and m  ACD = x + 28. What is m CAD?
18. In rhombus ABCD, the measure, in inches, of AB is 3x + 2 and BC is x + 12. Find the length of DC.
19. In the diagram below, quadrilateral STAR is a rhombus with diagonals SA and TR intersecting at E. ST = 3x + 30,
SR = 8x − 5, SE = 3z, TE = 5z + 5, AE = 4z − 8, m∠RTA = 5y − 2, and m∠TAS = 9y + 8. Find SR, RT, and m∠TAS .
Trapezoids
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Trapezoid—____________________________________________________________________
o
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_________—one of the parallel sides ( BC , AD )
o ______—one of the non-parallel sides ( AB , CD )
o Consecutive angles are supplementary, add up to 180 degrees (  A +  B = 180,  C +  D = 180)
Isosceles Trapezoid—Special trapezoid with two congruent legs
o Legs are congruent
o Base angles are congruent
o _______________ are congruent
Practice Problems:
20. Isosceles trapezoid ABCD has diagonals AC and BD. If AC  5x  13 and BD  11x  5, what is the value of x?
21. In the trapezoid below, find mS
22. In the trapezoid below, find mT
23. A set of five quadrilaterals consists of a square, a rhombus, a rectangle, an isosceles trapezoid, and a parallelogram.
Lu selects one of these figures at random. What is the probability that both pairs of the figure's opposite sides are
parallel?
24. In a certain quadrilateral, two opposite sides are parallel, and the other two opposite sides are not congruent. This
quadrilateral could be a
(A) rhombus
(C) square
(B) parallelogram
(D) trapezoid
Answer Key:
Fill-in-the-Blanks
Angle Relationships in Parallel Lines Cut by a Transversal
o Vertical angles; two angles that are in the same location at each intersection;  3 and  6 or  4 and  5;
alternate exterior angles; 180
Interior and Exterior Angles in a Polygon
o Regular polygon; (n – 2) × 180; 360
Parallelograms
o Parallel; congruent; opposite angles; bisect each other
Rhombuses, Rectangles, Squares
o Rhombus, right angles; congruent; square, congruent and perpendicular
Trapezoids
o Quadrilateral with only one pair of opposite sides that are congruent; base; leg; Isosceles, diagonals
Practice Problems
1. (B)
2. (A)
8. 135
9. 60
3. 65 degrees
10. 45
4. (A)
11. (A)
15. 75
17. 3
18. 117 19. 60
16. 50
5. 1080 6. 360
7. 75
12. 8
13. 30
20.
4
5
21. (D)
14. (B)