Post on 02-Jan-2016
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THE PROPERTIES OF PARALLELOGRAMS
1. Opposite sides are congruent (AB=DC)
2. Opposite angles are congruent (D=B)
3. Consecutive angles are supplementary (A+D=180)
4. If one angle is right, then all angles are right.
5. The diagonals of a parallelogram bisect each other.
6. Each diagonal of a parallelogram separates it into two congruent triangles.
A B
CD
Example 1AWXYZ is a
parallelogram. Find YZ.
Def. of segs.
Substitute the given values.
Subtract 6a from both sides and add 4 to both sides.
Divide both sides by 2.
YZ = XW
8a – 4 = 6a + 10
2a = 14
a = 7
YZ = 8a – 4 = 8(7) – 4 = 52
opp. s
ALTERNATE INTERIOR
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1 234
5 678
Interior angles that lie on different parallel lines and opposite sides of transversal. They are equal to each other!
ALTERNATE EXTERIOR Angles formed
outside the parallel lines and on opposite sides of transversal. They are equal!
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1 234
5 678
CORRESPONDINGAngles that lie on the same
side of the transversal and are situated the same way on two parallel lines. Think:
Four CORNERS. They are equal!
m
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1 234
5 678
CLASSIFYING TRIANGLES
Triangle – A figure formed when three noncollinear points are connected by segments.
E
DF
Angle
SideVertex
The sides are DE, EF, and DF.The vertices are D, E, and F.The angles are D, E, F.
BASE ANGLES THEOREM
If two sides of a triangle are congruent, then the angles opposite them are congruent.
If , thenACAB CB
CONVERSE OF BASE ANGLES THEOREM
If two angles of a triangle are congruent, then the sides opposite them are congruent.
If , thenCB ACAB
TRIANGLE SUM THEOREMThe measures of the three interior angles
in a triangle add up to be 180º.
x°
y° z°
x + y + z = 180°
The measure of the exterior angle is equal to the sum of two nonadjacent interior angles
1
2 3
m1+m2 =m3
Exterior Angle Theorem