Download Perpendicular Bisector Thm. if a point is on the perpendicular

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December 13, 2014
Midsegment Thm. ­ The midsegment of a triangle connects the midpoints of 2 sides of a triangle,
and is parallel to and 1/2 the length of the third side.
B
is a midsegment
ll
M
N
or 2MN = AC
A
C
Midpoint formula 22. Midsegment Thm.
23. Perpendicular Bisector Thm. Dec 13­8:25 AM
Perpendicular Bisector Thm.­ if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Converse of the Perpendicular Bisector Thm. ­ if a point is equidistant from both endpoints of a segment, then it is on the perpendicular bisector of the segment.
Dec 13­8:39 AM
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December 13, 2014
Angle Bisector Thm. ­ if a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.
A
D
E
B
C
Converse of the Angle Bisector Thm. ­ if a point is in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.
24. Angle Bisector Thm.
25. Polygon Formulas
Dec 13­8:40 AM
Formulas for Polygons
s = sum of interior angles
n = # of sides
1. s = (n­2)180 Polygon Angle­Sum Theorem
2. sum of exterior angles = 3600
Regular Polygons ­ a polygon that is equilateral and equiangular.
1. one interior angle = 2. 3. one exterior angle =
4. interior angle + exterior angle = 1800
Dec 13­8:41 AM
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December 13, 2014
Quadrilateral
Tw
o s
ets
of
pa
r
alle
t of
pa
rall
ed si
des
llel
es para
No sid
des
Parallelogram
1 se
Kite
l si
Trapezoid
Rectangle
Rhombus
Isosceles Trapezoid
Square
26. Quadrilaterals
27. Parallelogram Thms.
Dec 13­8:41 AM
PARALLELOGRAM ­ Quadrilaterals with BOTH pairs of opposite sides parallel.
Properties:
D
C
1. Thm: opposite sides are 2. Thm: opposite angles are
3. Thm: consecutive angles are supplementary
A
B
4. Thm: diagonals bisect each other
Dec 13­8:42 AM
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December 13, 2014
Ways of proving a quadrilateral is a parallelogram.
1. If BOTH pairs of sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.
(By Definition)
2. If BOTH pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.
3. If 1 pair of opposite sides of a quadrilateral are BOTH parallel and congruent, then the quadrilateral is a parallelogram. 4. If BOTH pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.
5. If the diagonals of the quadrilateral bisect each other, then the quadrilateral is a parallelogram.
page 371
28. Proving Parallelograms
29. Rhombus
Dec 13­8:43 AM
Rhombus ­ a parallelogram with consecutive sides Properties
1. All the properties of a hold.
2. All sides are
3. Diagonals are perpendicular
4. Diagonals bisect a pair of opposite angles
diagonal bisects so
5. Diagonals also divide the rhombus into 4 congruent triangles D
C
6
8 7
5
1
2
A
34
B
Dec 13­8:43 AM
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Rectangle ­ a parallelogram with a right angle
Properties
1. are right angles.
2.
B
C
M
D
A
30. Rectangle
31. Square
Dec 13­8:44 AM
Square ­ 1. A rectangle with all sides 2. A rhombus with one right angle.
Properties:
1. All properties of parallelograms hold.
2. All properties of rectangles hold.
3. All properties of rhombus hold.
Square ABCD
D
are right angles
C
E
1
A
B
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December 13, 2014
Trapezoid ­ a quadrilateral with one pair of opposite sides parallel. The parallel sides are called the bases. The non parallel sides are called legs.
Base
A
Leg
B
2
Leg
1
D
C
Base
Isosceles Trapezoid ­ trapezoid with congruent legs.
D
Properties:
1. Legs are 2. Diagonals are
3. Base angles are C
A
B
32. Trapezoid
33. Kite
Dec 13­8:45 AM
Kite ­ no parallel sides and 2 pair of consecutive congruent sides.
ABCD is a kite
B
Property: 1. The diagonals of a kite are
perpendicular.
C
A
D
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December 13, 2014
Trapezoid Midsegment Theorem
R
base 1
A
M
T
N
P
base 2
1. The midsegment is ll to the base
2. The length of the midsegment is
34. Trapezoid Midsegment Thm.
35. Dec 13­8:46 AM
Dec 13­8:51 AM
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