Term
|
Definition
A quad. with both pairs of opposite sides ǁ (Usually shown by a tilted rectangle.)
Pg. 167 |
|
|
Term
Theorem 5-1
Opp. sides of a parallelogram |
|
Definition
Opposite sides of a parallelogram are ≅
Pg. 167 |
|
|
Term
Theorem 5-2
Opp. <s of a parallelogram |
|
Definition
Opposite <s of a parallelogram are ≅
Pg. 167 |
|
|
Term
Theorem 5-3
Diagonals of a parallelogram |
|
Definition
Diagonals of a parallelogram bisect each other.
Pg. 167 |
|
|
Term
Theorem 5-4
Starting with both pairs of opp. sides of a quad. ≅ |
|
Definition
If both pairs of opposite sides of a quad. are ≅, then the quad. is a parallelogram
Pg. 172 |
|
|
Term
Theorem 5-5
Starting with one pair of opp. sides of a quad. both ≅ and ǁ |
|
Definition
If one pair of opp. sides of a quad. are both ≅ and ǁ, then the quad. is a parallelogram.
Pg. 172 |
|
|
Term
Theorem 5-6
Starting with both pairs of opp. sides of a quad. ≅ |
|
Definition
If both pairs of opp. <s of a quad. are ≅, then the quad. is a parallelogram.
Pg. 172 |
|
|
Term
Theorem 5-7
Starting with diagonals of a quad bisect each other |
|
Definition
If the diagonals of a quad. bisect each other, then the quad. is a parallelogram.
Pg. 172 |
|
|
Term
| Five Ways to Prove a Quad is a Parrallelogram |
|
Definition
1. Show both pairs of opp. sides ǁ
2. Show both pairs of opp. sides ≅
3. Show one pair opp. Sides ≅ and ǁ
4. Show both pairs opp. <s ≅
5. Show diagonals bisect each other
Pg. 172 |
|
|
Term
Theorem 5-8
Starting with ǁ lines |
|
Definition
If two lines are ǁ, then all points on one line are equidistant from the other line.
Pg. 177 |
|
|
Term
Theorem 5-9
ǁ lines and ≅ segments |
|
Definition
If three ǁ lines cut off ≅ segments on one transversal, then they cut off ≅ segments on every transversal.
Pg. 177 |
|
|
Term
Theorem 5-10
Midpoint of a side of a ∆ and ǁ lines |
|
Definition
A line that contains the midpoint of one side of a ∆ and is ǁ to another side passes through the midpoint of the third side.
Pg. 178 |
|
|
Term
Theorem 5-11
Joining midpoints of two sides of a ∆ |
|
Definition
The segment that joins the midpoints of two sides of a ∆
1. is ǁ to the third side
2. is half as long as the third side
Pg. 178 |
|
|
Term
|
Definition
A quad. with four right <s
Pg. 184 |
|
|
Term
|
Definition
A quad. with four ≅ sides (Diamond)
Pg. 184 |
|
|
Term
|
Definition
A quad. with four right <s and four ≅ sides
*This could be called a rectangle or a rhombus
Pg. 184 |
|
|
Term
Theorem 5-12
Diagonals of a Rectangle |
|
Definition
The diagonals of a rectangle are ≅
Pg. 185 |
|
|
Term
Theorem 5-12
Diagonals of a rhombus |
|
Definition
The diagonals of a rhombus are ┴
Pg. 185 |
|
|
Term
Theorem 5-14
Diagonals and <s of a rhombus |
|
Definition
Each diagonal of a rhombus bisects two <s of the rhombus.
Pg. 185 |
|
|
Term
Theorem 5-15
Midpoint of the hyp. of a right ∆ |
|
Definition
The midpoint of the hyp. of a right ∆ is equidistant from the three vertices.
Pg. 185 |
|
|
Term
Theorem 5-16
Parallelogram and rt. < |
|
Definition
If an < of a parallelogram is a right <, then the parallelogram is a rectangle.
Pg. 185 |
|
|
Term
Theorem 5-17
Consecutive sides ≅ |
|
Definition
If two consecutive sides of a parallelogram are ≅, then the parallelogram is a rhombus.
Pg. 185 |
|
|
Term
|
Definition
A quad. with exactly one pair of ǁ sides
Pg. 190 |
|
|
Term
Base & Legs
of a trapezoid |
|
Definition
Bases- ǁ sides of the trapezoid
Legs- the other two sides
Pg. 190 |
|
|
Term
|
Definition
A trapezoid with ≅ legs
Pg. 190 |
|
|
Term
Theorem 5-18
Base <s of an isosceles trapezoid |
|
Definition
Base <s of an isosceles trapezoid are ≅
Pg. 190 |
|
|
Term
|
Definition
| The segment that joins the midpoints of the legs. |
|
|
Term
Theorem 5-19
Median of a trapezoid |
|
Definition
The median of a trapezoid
1. is ǁ to the bases
2. has a length equal to the average of the base lengths
Pg. 191 |
|
|
