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Lesson 16, page 1 of 10 L Leessssoonn (^1166) Glencoe Geometry Chapter 6.3 & 6. Rectangles, Squares, & Rhombi
Remember: _____________ are closed geometric shapes. ____________________are 4-sided polygons.
_______________are quadrilaterals with both
pairs of opposite sides parallel to each other.
Today we take a closer look at three special types of Parallelograms: Rectangles, Squares, and Rhombi.
Definition:
A rectangle is a quadrilateral with four right angles.
A Rectangle’s diagonals have a special property: THEY ARE CONGRUENT!!
A B
C
Because rectangle
ABCD is a
parallelogram,
AE ≅EC & DE ≅ EB
E
D
BUT...
Since it is a rectangle, we also know that AC ≅ BD
This forms two sets of congruent isosceles
triangles:! AED ≅! making all the half-
diagonal segments congruent to each other!!
BEC
Example:
In rectangle WXYZ, m ∠ 1 = 40 ". Find m∠ 2.
W X 2 V (^1)
3 Z Y
A. 20 B. 70 C. 140 D. 40
Definition:
C D
A B
A square is a quadrilateral with four right angles, and four congruent sides.
AB ≅ BD ≅ DC ≅CA
Squares have all the same properties of rectangles and some additional ones to boot! The diagonals
- are perpendicular
- bisect a pair of opposite angles
6 8
5 7
2 4
1 3 E
C^ D
A B
The slopes ofeach other. AD and BC are negative reciprocals of
The diagonals form 4 congruent isosceles triangles! What a deal!!
are congruent and equalm^ ∠^1 =^ m^ ∠^3 =^45 "^. If fact, all the numbered angles 45 ".
Definition:
A rhombus is a quadrilateral with four four congruent sides.
Unlike the rectangle and the square, the angles of rhombus need not be right angles, but other than that, it’s properties are similar to the square. L O
E V
7 8 6
5
3 4
1 2
K
V
1. LO ≅ OV ≅ VE ≅EL
2. LV ⊥OE
- ∠ 1 ≅ ∠ 3 ≅ 6 ≅ 8 and ∠ 5 ≅ ∠ 7 ≅ ∠ 2 ≅ ∠ 4 (but these two sets are not necessarily congruent to each other).
Example:
In rhombus EFGH, m∠1 = 57°, HE = 13 , HP = 12.
What is m ∠2? What is PE?
2 3 4
1
P
H
G
F
E
- The most specific description of the quadrilateral below is ________.
A. square B. rhombus C. rectangle D. parallelogram
- Choose the most precise description for the figure shown. 6 m
6 m 90 "
A. parallelogram B. square C. rhombus D. quadrilateral
6 m
6 m
Some images and problems from www.glencoe.com
