activity 15. quadrilateral a polygon with 4 sides
TRANSCRIPT
Activity 15
Quadrilateral
• A polygon with 4 sides
Special Quadrilaterals• Parallelogram:
quadrilateral with both sides parallel
• Rhombus:
a parallelogram with 4 congruent sides
• Rectangle:
a parallelogram with 4 right angles
• Square:
a parallelogram with 4 congruent sides and 4 right angles
• Kite:
A quadrilateral with two pairs of adjacent sides congruent
• Trapezoid:
a quadrilateral with exactly one pair of parallel sides
15.3: Properties of Parallelograms
Parallelogram
• A quadrilateral with both pairs of opposite sides parallel
Properties:
1. Opposite sides are congruent (thm)
2. Opposite angles are congruent (thm)
3. Consecutive angles are supplementary
4. Diagonals bisect each other (thm)
5. If there is one right angle, then there are 4 right angles
Find the variables/measurements1. b = ?
2. mRST = ?
3. mSTU = ?
4. mSTR = ?
Given Parallelogram JKLM• Find X and Y with JN = 6y + 1, NK = x + 7,
NL = 4y + 9, and MN = 2x – 5
J K
LM
N
Theorem 6-4• If 3 or more parallel lines are cut off by
congruent segments on one transversal, then they cut off congruent segments on every transversal.
8
8
8 12.5H
B
C
D
E
F
G
A
Find EH.
12.5
12.5
Example• Find a and b.
5b + 5
3a – 5
28
15.4 Special Parallelograms
Rhombi• A parallelogram with all four sides congruent
Rhombus Properties:
• Diagonals of a rhombus are perpendicular
• Each diagonal bisects a pair of opposite angles.
Parallelogram Properties:
• Opposite sides congruent and parallel
• Opposite angles congruent
• Diagonals bisect each other
Find the x, y, mYKR, mRYP of rhombus RYZP with PK=3x – 1, PY=16, RK=4y+1, ZK=7y – 14, and mZRY=43
Rectangles
• A parallelogram with four right angles
Rectangle Properties:
• Diagonals of a rectangle are congruent Parallelogram Properties:
• Opposite sides congruent and parallel
• Opposite angles congruent
• Diagonals bisect each other
R S
TU
Find the x and mCDB, mADB, mCBD of rectangle ABCD
Square
• A parallelogram with 4 congruent sides and 4 right angles
• Has all properties of parallelograms, rectangles, and rhombi– Opposite sides congruent and parallel– Diagonals are congruent, perpendicular, bisect
each other and bisect pairs of opposite angles
Trapezoids
Trapezoid
• A quadrilateral with exactly one pair of parallel sides
• NOT a parallelogram… does not have properties of one
• Parallel sides are called bases
• Nonparallel sides are called legs
base
base
leg
leg
Base Angles of a Trapezoid• There are 2 pairs of base angles
• Each pair of base angles are formed by the same base and non-common legs
Trapezoid WXYZ
Y
W X
Z
Isosceles Trapezoid
• A trapezoid with legs congruent to each other
Properties of An Isosceles Trapezoid:
• Both pairs of base angles are congruent
• Non-congruent angles are supplementary
• Diagonals of an isosceles trapezoid are congruent
Find mO and
mMNQ if MNOP
is an isosceles trapezoid
Median of a Trapezoid
• Segment that joins the midpoints of the legs of a trapezoid
• Parallel to the bases
• Median equals ½ the sum of the bases
UV = (½)(WX + ZY)
Y
W X
Z
U V
Find IJ if FG=16 and EH=43.
Find PL.
Find the coordinates for the endpoints of the median of the trapezoid ABCD with
A(1,3), B(5,0), C(8,-5), and D(-4, 4).
Other Quadrilaterals:
Trapeziums and Kites
Trapezium
- Quadrilateral with no two sides parallel
Kite• A quadrilateral with exactly two distinct pairs of adjacent congruent sides
Important Facts:
• Diagonals of a kite are perpendicular• One pair of opposite angles are congruent• Other two angles bisected by diagonals• Look for pairs of congruent triangles!
Find x and y.J
K
L
M
2x + 55x – 16
6x – 19 -y +
20
• Find m1 and m2.