geometry today: class attendance / announcements 6.4 vocabulary review warm-up 6.4 notes / practice...
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GeometryGeometry
Today:• Class Attendance
/ Announcements• 6.4 Vocabulary
Review• Warm-Up• 6.4 Notes /
Practice• Begin Homework
Every moment in planning saves 3 or 4 in execution.
Crawford Greenwalt
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WARM-UPWARM-UP
What are the properties of a parallelogram?
6.3
6.4 – Rhombuses, 6.4 – Rhombuses, Rectangles, & SquaresRectangles, & Squares
Objectives:1.Know special parallelograms2.Know properties of special
parallelograms
Vocabulary:square, rhombus, rectangle
VocabularyVocabulary
Rectangle – a quadrilateral with 4 right angles
6.4
RECTANGLE FACTS:RECTANGLE FACTS:
Has all 5 properties of a parallelogram+ Has four right angles.+ Diagonals are congruent.
+ A parallelogram is a + A parallelogram is a rectangle iff the rectangle iff the diagonals are congruent.diagonals are congruent.
6.4
7 properties total7 properties total
VocabularyVocabulary
Rhombus – a quadrilateral with 4 congruent sides
6.4
RHOMBUS FACTS:RHOMBUS FACTS:
+ Diagonals are + Diagonals bisect angles.A parallelogram is a rhombus iff the A parallelogram is a rhombus iff the
diagonals are perpendicular.diagonals are perpendicular.
A parallelogram is a rhombus iff the A parallelogram is a rhombus iff the diagonals bisect the angles.diagonals bisect the angles.
6.4
Has all 5 properties of a parallelogram+ Has four congruent sides.
8 properties 8 properties totaltotal
VocabularyVocabulary
Square – a quadrilateral with 4 right angles and 4 congruent sides (both a rhombus and a rectangle)
6.4
SQUARE FACTSSQUARE FACTS
Has all 5 properties of a parallelogram
Has all properties of a rectangle (additional 2 properties).
6.4
10 properties total10 properties total
Has all properties of a rhombus (additional 3 properties).
Break TimeBreak Time
Take a few minutes to get up, stretch out, or try the following rebus puzzles.
To see redTo see red Travel Travel overseasoverseas
Quadrilaterals
(4 sides)
Parallelograms
(opp. sides ll)
Rhombus(all sides )
Rectangles(all right ’s)
Square(Rect & Rhomb)
6.6
• What type of quadrilateral is ABCD?
• Parallelogram• Rectangle
A B
CD
QUESTIONS ABOUT SPECIAL QUESTIONS ABOUT SPECIAL QUADRILATERALSQUADRILATERALS
Answer each question with A, S, N for always, sometimes, and never true.
1. A rectangle is a square
2. A square is a rhombus
3. A rectangle is a parallelogram
4. A rectangle is a rhombus6.4
Property ll rect
rhm
sqr kite
trp istrp
Both pairs of opposite sides parallel
Exactly 1 pair of opposite sides parallel
Diagonals perpendicular
Diagonals congruent
Diagonals bisect each other
Both pairs of opposite sides are congruent
Exactly one pair of opposite sides are congruent
All sides are congruent
Both pairs of opposite angles are congruent
Exactly one pair of opposite angles are congruent
All angles are congruent
Property ll rect
rhm
sqr kite
trp istrp
Both pairs of opposite.sides parallel XExactly 1 pair of opposite sides parallel
Diagonals perpendicular
Diagonals congruent
Diagonals bisect each other XBoth pairs of opposite sides are congruent XExactly one pair of opposite sides are congruent
All sides are congruent
Both pairs of opposite angles are congruent XExactly one pair of opposite angles are congruent
All angles are congruent
Property ll rect
rhm
sqr kite
trp istrp
Both pairs of opposite.sides parallel X XExactly 1 pair of opposite sides parallel
Diagonals perpendicular
Diagonals congruent XDiagonals bisect each other X XBoth pairs of opposite sides are congruent X XExactly one pair of opposite sides are congruent
All sides are congruent
Both pairs of opposite angles are congruent X XExactly one pair of opposite angles are congruent
All angles are congruent X
Property ll rect
rhm
sqr kite
trp istrp
Both pairs of opposite.sides parallel X X XExactly 1 pair of opposite sides parallel
Diagonals perpendicular XDiagonals congruent XDiagonals bisect each other X X XBoth pairs of opposite sides are congruent X X XExactly one pair of opposite sides are congruent
All sides are congruent XBoth pairs of opposite angles are congruent X X XExactly one pair of opposite angles are congruent
All angles are congruent X
Property ll rect
rhm
sqr kite
trp istrp
Both pairs of opposite.sides parallel X X X XExactly 1 pair of opposite sides parallel
Diagonals perpendicular X XDiagonals congruent X XDiagonals bisect each other X X X XBoth pairs of opposite sides are congruent X X X XExactly one pair of opposite sides are congruent
All sides are congruent X XBoth pairs of opposite angles are congruent X X X XExactly one pair of opposite angles are congruent
All angles are congruent X X
QUESTIONS ABOUT SPECIAL QUESTIONS ABOUT SPECIAL QUADRILATERALSQUADRILATERALS
List all the special quadrilaterals that have each property:
1. Diagonals are congruent
2. Diagonals are perpendicular
3. Consecutive angles are supplementary.
4. Regular polygon
6.4
MNOP is a rectangle with interior point A. If MA = 6x + 4 and PA = 7x – 4, find PN.
6.4
A
D C
B
5x +
8° 3x + 2°
6.4
Find x and y, such that ABCD is a rectangle.
6y + 2°
QRST is a rhombus. Find x and y, if m1 = y2 – 54, m2 = 5x + 7 and m3 = 7x – 1.
Q
R
T
S
23
6.4
1
Is ABCD a square, rectangle or rhombus?
D
A
C
Bx + 7
3y +
36.4
2x – 4
4y –
2
10z + 5°8z +
13°
GeometryGeometry
Homework:• 6.4 pgs. 351-
352 #16-38
• Chapter 6 Test Chapter 6 Test on Wednesdayon Wednesday
Every moment in planning saves 3 or 4 in execution.
Crawford Greenwalt