Download Teacher Geometry Notes 2.3 Segment and Angle Relationships

Teacher Geometry Notes 2.3 Segment and Angle Relationships
Vocabulary:
(1)
Congruent
(a)
Two segments are congruent, ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐷, if they have the same length.
(b)
Two angles are congruent, ∢𝑃 ≅ ∢𝑄, if they have the same measure.
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(2)
The midpoint of a segment is the point that divides the segment into two congruent segments.
(3)
A segment bisector is a segment, ray, line or plane that intersects a segment at its midpoint.
(4)
An angle bisector is a ray that divides the angle into two congruent angles.
(5)
Perpendicular
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(a)
Two lines are perpendicular (⊥) if they intersect to form a right angle.
(b)
A line is ⊥to a plane if it is ⊥ to each line in the plane that intersects it.
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***Definitions – can always be interpreted “forward” and “backward”***
i.e. – “If two segments have the same measure, then they are ≅.” AND “If two segments are ≅
then they have the same measure”
The Distance Formula – used to compute the distance between points in a coordinate plane.
(a)
Let 𝐴 = (𝑥1 , 𝑦1 ) and 𝐵 = (𝑥2 , 𝑦2 ) be points on a coordinate plane. The distance
between A and B is:
𝐴𝐵 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
(E1.)
Find the distance between (−1,2)𝑎𝑛𝑑 (2, −4).
𝐴𝐵 = √(2 − −1)2 + (−4 − 2)2 = √32 + (−6)2 = √9 + 36 = √45 = 3√5
(P1.)
Find the distance between (0, 4)𝑎𝑛𝑑 (2, 3).
𝐴𝐵 = √(2 − 0)2 + (3 − 4)2 = √22 + (−1)2 = √4 + 1 = √5