Understand, use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.
MM1G3d
Jan 16, 2016
Understand, use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite. MM1G3d. Vocabulary. Parallelogram: A quadrilateral with both pairs of opposite sides parallel. - 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
Understand, use and prove properties of and relationships among special quadrilaterals:
parallelogram, rectangle, rhombus, square, trapezoid, and kite.
Vocabulary
Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
Rhombus: a parallelogram with four congruent sides.
Rectangle: a parallelogram with four right angles.
Square: a parallelogram with four congruent sides and four right angles.
Corollaries
A quadrilateral is a rhombus if and only if it has four congruent sides.
A quadrilateral is a rectangle if and only if it has four right angles.
A quadrilateral is a square if and only if it is a rhombus and a rectangle.
Example 1
Classify the quadrilateral.
7 7
77 73° This quadrilateral is a rhombus becauseall sides are congruent.
Example 2
Classify the quadrilateral.
The quadrilateral is a rectangle becauseall angles are right angles.
We do not know if it is a square becausewe do not know if all of the sides arecongruent.
Rhombus
A parallelogram is a rhombus if and only if its diagonals are perpendicular.
Rhombus
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
5353
5353
127
127127
127
Rectangle
A parallelogram is a rectangle if and only if its diagonals are congruent.
A
D C
B
AC is congruent to BD so ABCDis a rectangle.
Example 3 The diagonals of rectangle EFGH intersect at T.
Given that m<GHF = 40° and EG = 16, find the indicated variables.
H G
FE
xz
y
T
Find x.
EFGH is a rectangle so the diagonals are congruent.EG = 16 so FH = 16.EFGH is a parallelogram so the diagonalsbisect each other.Therefore, x = FT = 8.
Example 3 The diagonals of rectangle EFGH intersect at T.
Given that m<GHF = 40° and EG = 16, find the indicated variables.
H G
FE
xz
y
T
Find y.
HT and GT are equal, so the anglesopposite them are equal.Therefore, m<GHF = m<HGE.
40
Example 3 The diagonals of rectangle EFGH intersect at T.
Given that m<GHF = 40° and EG = 16, find the indicated variables.
H G
FE
xz
T
Find y.
HT and GT are equal, so the anglesopposite them are equal.Therefore, m<GHF = m<HGE.Since mGHF = 40°, m<HGE = 40°.40 40
Example 3 The diagonals of rectangle EFGH intersect at T.
Given that m<GHF = 40° and EG = 16, find the indicated variables.
H G
FE
xz
40
T
Find z.
ΔEHG is a right triangle with <Hbeing the right angle.
z + 90 + 40 = 180 z + 130 = 180 – 130 – 130
z = 50
Assignment
Textbook: p.319-320 (1-28)