Aim: Properties of Square & Rhombus Course: Applied Geo. Do Now: Aim: What are the properties of a rhombus and a square? Find the length of AD in rectangle ABCD, if AB = 2 and diagonal BD = 4. A rectangle has 4 right angles. 4 2 x B C D A a 2 + b 2 = c 2 Pythagorean Theorem a 2 + b 2 = c 2 ABD is a right triangle 2 2 + x 2 = 4 2 4 + x 2 = 16 x 2 = 12 12 3.46 x
14
Embed
Aim: What are the properties of a rhombus and a square?
Aim: What are the properties of a rhombus and a square?. Pythagorean Theorem. a 2 + b 2 = c 2. Do Now:. Find the length of AD in rectangle ABCD, if AB = 2 and diagonal BD = 4. ABD is a right triangle. A rectangle has 4 right angles. a 2 + b 2 = c 2. 2 2 + x 2 = 4 2. - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Aim: Properties of Square & Rhombus Course: Applied Geo.
Do Now:
Aim: What are the properties of a rhombus and a square?
Find the length of AD in rectangle ABCD, if AB = 2 and diagonal BD = 4.
A rectangle has 4 right angles.A rectangle has 4 right angles.
42
x
B C
DA
a2 + b2 = c2
Pythagorean Theorem
a2 + b2 = c2
ABD is a right triangle
22 + x2 = 42
4 + x2 = 16x2 = 12
12 3.46x
Aim: Properties of Square & Rhombus Course: Applied Geo.
A B
D C
Properties of a Rhombus
A rhombus has all the properties of a parallelogram,A rhombus has all the properties of a parallelogram,
PLUS,A rhombus is equilateral.A rhombus is equilateral.
The diagonals of a rhombus are perpendicular to each other.The diagonals of a rhombus are perpendicular to each other.
A rhombus is a parallelogram that has two congruent consecutive sides.
A rhombus is a parallelogram that has two congruent consecutive sides.
The diagonals of a rhombus bisect its anglesThe diagonals of a rhombus bisect its angles
Aim: Properties of Square & Rhombus Course: Applied Geo.
Properties of a QuadrilateralsProperty Parallel. Rectangle Rhombus
All sides are
Opposite sides are
Opposite sides are | |
Opposite angles are
All angles are right
Diagonals bisect each other
Diagonals are
Diagonals are
Each Diagonal bisects opposite
Aim: Properties of Square & Rhombus Course: Applied Geo.
Model Problem
Find the measures of the numbered angles in the rhombus
500
1
324
1 = 900 Diagonals of a rhombus are Perpendicular
2 = 500 Alternate Interior s
3 = 500 Diagonals of rhombus bisect the s
4 = 400 The sum of the s of a equal 1800
The diagonals of a rhombus are perpendicular to each other.
The diagonals of a rhombus are perpendicular to each other.
900
500
500400
900
Aim: Properties of Square & Rhombus Course: Applied Geo.
Regents Question
In the diagram below of rhombus ABCD, m∠C = 100.
What is m∠DBC? 40o
40o
Aim: Properties of Square & Rhombus Course: Applied Geo.
Model Problem
Find the value of the variables (2x)º
(x + y)º(3z)º
Since all sides are congruent this quadrilateral is a rhombus.
Property Parallel. Rectangle Rhombus
2x = 90 x = 453z = 90 z = 30
x + y = 90 45 + y = 90 y = 45
Diagonals are
Aim: Properties of Square & Rhombus Course: Applied Geo.
Model Problem
Explain how and why ABCD is a rhombus
Given: ABCD is a parallelogramAB = 2x + 1, DC = 3x – 11, AD = x + 13
Plan: Show that 2 consecutive sides are congruent. (AB AD)
A B
D C
1) Since ABCD is a parallelogram, opposite sides are equal in length.DC = AB 3x – 11 = 2x + 1
3x – 2x = 11 + 1 x = 12
2) Substitute x = 12 to find the length of AB and AD: AB = 2x + 1 = 2(12) + 1 = 25
AD = x + 13 = 12 + 13 = 25
AB AD. Since parallelogram ABCD hastwo consecutive congruent sides, it’s a rhombus.
Aim: Properties of Square & Rhombus Course: Applied Geo.
Do Now:
Aim: What are the properties of a rhombus and a square?
In rhombus KLMN, KL = 3x, LM = 2(x + 3). Find the length of each side of the rhombus.
K N
L M
Aim: Properties of Square & Rhombus Course: Applied Geo.
Properties of a Square
A square is a rectangle that has two congruent sides.
A square is a rectangle that has two congruent sides.
C
B
D
A
A square has all the properties of a rectangle,A square has all the properties of a rectangle,
PLUS,
A square has all the properties of a rhombus.A square has all the properties of a rhombus.
Aim: Properties of Square & Rhombus Course: Applied Geo.
Properties of a SquareProperty Parallel. Rhombus Rectangle Square
All sides are
Opposite sides are
Opposite sides are | |
Opposite angles are
All angles are right
Diagonals bisect each other
Diagonals are
Diagonals are
Each Diagonal bisects opposite
Aim: Properties of Square & Rhombus Course: Applied Geo.
Model Problem
ABCD is a square with diagonal BD. Determine if True or False.
A. AB BC
B. AB CD
C. AB AC
D. 1 2
E. 1 3
F. B 4
G. ABC is isosceles
H. ABC is right triangle
I. ABC ACD
A B
CD
12
34
Aim: Properties of Square & Rhombus Course: Applied Geo.
Model Problem
Find the value of the variables.
In a square: diagonals are to each otherdiagonals bisect opposite angles
In a square: diagonals are to each otherdiagonals bisect opposite angles
x = 5
19x 6z
1 = 3y – 6
y = 32x = 7.5
Aim: Properties of Square & Rhombus Course: Applied Geo.
Model Problem
ABCD is a square. If AB = 8x – 6 and BC = 5x + 12, find the length of each side of the square.
Which statement is false?
a) a square is a rectangle
b) a square is a rhombus
c) a rhombus is a square
d) a square is a parallelogram
Aim: Properties of Square & Rhombus Course: Applied Geo.
Model Problem
In square ABCD diagonal AC is drawn. How many degrees are there in the measure of ACB?
If the side of a square is 4, find the length of the diagonal.