2.19 - Classify Parallelograms 1 Ringer Bell 1) 2) 12/10/09.
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Transcript of 2.19 - Classify Parallelograms 1 Ringer Bell 1) 2) 12/10/09.
2.19 - Classify Parallelograms 1
Ringer Bell1) 2)
12/10/09
2.19 - Classify Parallelograms 2
2.19
Classify Parallelograms
2.19 - Classify Parallelograms 3
Rectangles
Opp. sides are ||. Opp. sides are . Opp. Angles are . Consecutive angles are supplementary. Diagonals bisect each other.
Definition: A rectangle is a parallelogram with four right angles.
A rectangle is a special type of parallelogram. Thus a rectangle has all the properties of a parallelogram.
2.19 - Classify Parallelograms 4
Properties of Rectangles
Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles.
If a parallelogram is a rectangle, then its diagonals are congruent.
E
D C
BA
Theorem:
Converse: If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle.
2.19 - Classify Parallelograms 5
Examples…….1. If AE = 3x +2 and BE = 29, find the value of x.
2. If AC = 21, then BE = _______.
3. If m<1 = 4x and m<4 = 2x, find the value of x.
4. If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6.
m<1=50, m<3=40, m<4=80, m<5=100, m<6=40
10.5 units
x = 9 units
x = 18 units
6
54
321
E
D C
BA
2.19 - Classify Parallelograms 6
Rhombi &
Squares
2.19 - Classify Parallelograms 7
RhombusDefinition: A rhombus is a parallelogram with four congruent sides.
Since a rhombus is a parallelogram the following are true: Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other
≡
≡
2.19 - Classify Parallelograms 8
Properties of a RhombusTheorem: The diagonals of a rhombus are perpendicular.
Theorem: Each diagonal of a rhombus bisects a pair of opposite angles.
2.19 - Classify Parallelograms 9
Rhombus Examples .....Given: ABCD is a rhombus. Complete the following.
1. If AB = 9, then AD = ______.
2. If m<1 = 65, the m<2 = _____.
3. m<3 = ______.
4. If m<ADC = 80, the m<DAB = ______.
5. If m<1 = 3x -7 and m<2 = 2x +3, then x = _____.
54
3
21E
D C
BA9 units
65°
90°
100°
10
2.19 - Classify Parallelograms 10
Square
Opposite sides are parallel. Four right angles. Four congruent sides. Consecutive angles are supplementary. Diagonals are congruent. Diagonals bisect each other. Diagonals are perpendicular. Each diagonal bisects a pair of opposite angles.
Definition: A square is a parallelogram with four congruent angles and four congruent sides.
Since every square is a parallelogram as well as a rhombus and rectangle, it has all the properties of these quadrilaterals.
2.19 - Classify Parallelograms 11
Squares – Examples…...Given: ABCD is a square. Complete the following.
1. If AB = 10, then AD = _____ and DC = _____.
2. If CE = 5, then DE = _____.
3. m<ABC = _____.
4. m<ACD = _____.
5. m<AED = _____.8 7 6 5
4321
E
D C
BA10 units 10 units
5 units
90°
45°
90°
2.19 - Classify Parallelograms 12
Homework All four assignments are due tomorrow.
NO EXCEPTIONS