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Class Notes: Unit 2
1. Complementary angles are angles whose angle measure adds up to
90°.
2. Supplementary angles
Supplementary angles are angles whose angle measure adds up to 180°.
3. Whole Part Axiom: The whole is equal to the sum of its parts.
4. Vertical Angles: Vertical angles are a pair of opposite angles formed by intersecting lines.
Vertical angles are/6 always congruent. So, in this figure,
1
3 and
2
4.
5. Linear pairs
Linear pairs of angles add up to 180 degrees
6. Angle pairs formed by parallel lines cut by a transversal
When two parallel lines are cut by a third line, the third line is called the transversal. In the
example below, eight angles are formed when parallel lines m and n are cut by a transversal
line, t.
Vertical pairs:
1 and 4,
2 and 3,
5 and 8,
6 and 7
Pairs of vertical angles are congruent.
Alternate interior angles: Two interior angles on the opposite sides of the
transversal are alternate interior angles. Interior angles are congruent.
4 = 5,
3= 6
Alternate exterior angles: Two exterior angles on the opposite sides of
the transversal are alternate exterior angles.
Alternate exterior angles are congruent.
1= 8
2=
7
Corresponding angles: Two angles, one in the interior and one in the
exterior that are on the same side of the transversal are corresponding
angles.
Corresponding angles are congruent.
1 = 5,
3 = 7,
2 = 6,
4= 8
Same side Interior angles: Their sum is 180 degrees.
Class work:
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There are six important properties of parallelograms to k
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Opposite sides are congruent (AB = DC).
Opposite angels are congruent (D = B).
Consecutive angles are supplementary (A + D = 180°).
If one angle is right, then all angles are right.
The diagonals of a parallelogram bisect each other.
Isosceles Triangle
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In a triangle, if two sides are equal, then the angles opposite the equal sides are also
equal. (OR)
In an isosceles triangle, the angles opposite the equal sides are equal.
If in ABC, AB = AC then C = B
Equilateral Trainable
In an equilateral all its three sides are equal and its three angles are equal.
Median
A line segment from a vertex (corner point) to the midpoint of the opposite side.
In isosceles and equilateral triangles, the median bisects the angle at the
vertex whose two adjacent sides are equal.
A centroid of a triangle is the point where the three medians of the triangle meet.
AG = 2/3 AD,
GD = 1/3 AD
CG = 2/3 CF
GF = 1/3 CF
BG = 2/3 BE
GE = 1/3 BE