Download (Geometry) Lines and Angles

Geometry Definitions
Line: Is determined by two distinct end points and extends indefinitely in both directions. Perpendicular Lines: Intersecting lines that form right angles. Parallel Lines: Lines that never intersect or cross each other. Ray: A part of a line that has only one endpoint. End Point: Is the point at which a ray starts. Angles: Two rays joined at the same end point. Vertex: Is the point at which the two rays meet. Sides: What the sides of the ray are called. Right Angles: an angle that is exactly 90 degrees
Straight Angle: One angle that equals 180° Basically, a straight angle is a straight line. Vertical Angles: Adjacent Angles: Vertical angles are opposite angles. They will form two acute angles and two obtuse angles.  d and  b are vertical obtuse angle. They have the same measure  a and  c are vertical acute angles. They have the same measure
Adjacent Angles are two angles that share a common side. They are also supplementary angles, which means, the measure of the sums of their angles must equal 180 degrees. Adjacent Angles  a and  d
Acute Angles: one angle between 0· and 90· degrees.  a and  b
 b and  c
 d and  c
Complementary Angles: Two angles whose measures add up to 90o. Obtuse Angles: One angle between 90· and 180· degrees. Supplementary Angles: Two angles whose measures add up to 180°. Transversal Two parallel lines intersected by a transversal form corresponding pairs of angles that are congruent. Several types of angles are formed: alternate interior, alternate exterior , corresponding and vertical angles. Triangles: The sum of the interior angles of a triangle equal 180° Saved: Geometry Definitions – Lines & Angles-1
Alternate Interior Angles For any pair of parallel lines intersected by a third line, the transversal, alternate interior angles are formed. Alternate interior angles have the same degree. o  r
p  q
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Similar
Two polygons are similar if their corresponding sides are proportional. Similar Figures have the
same shape, but not necessarily the same size.
For Example: The triangles below are similar. Therefore, the measures of their corresponding
angles are equal, and the corresponding sides are in proportion.
Side AB corresponds to side DE
Side AC corresponds to side DF
Side BC corresponds to side EF
AB AC

DE DF

6 10

n 5
6 x 5  10n
3  n {the length of side DE is 3cm}
Alternate Exterior Angles
For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram
below, angle A and angle D are called alternate exterior angles. Alternate exterior angles have the same
degree measurement. Angle B and angle C are also alternate exterior angles.
n  o
m t
Corresponding Angles
Corresponding angles are two angles that are on the same side of the transversal. Both are acute angles or
both are obtuse angles. They have the same measure.
Corresponding Angles
Study Tip: To help you remember this rule, think of corresponding angles as top-top and bottom-bottom
Top Angles
Top Angles
m q
n  r
Bottom Angles
Bottom Angles
o  s
p  t
Corresponding Interior Angles
Angles on the same side of the transversal, and inside the parallel lines are supplementary angles, and
therefore the sum of their measures equals 180 degrees.
 o   q are corresponding interior angles
 p   r are corresponding interior angles
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