This post is a part of [
GRE MATH BOOK]
Frequency of the concepts tested:
HighDefinitionA. Lines, Line Segments, Rays, and Angles
1. Line‐is a set of points extending indefinitely in two directions.
2. Line segment‐is a piece of a line with two endpoints.
3. Ray‐is a part of a line with one endpoint.
4. Angle‐is made up of two rays that share the same endpoint calls vertex.
B. Angels as Acute, Right, Obtuse, or Straight
1. Acute Angle‐is an angle whose measure is between 0° and 90°.
2. Obtuse Angle‐ is an angle whose measure is between 90° and 180°.
3. Right Angle‐is an angle that measures 90°.
4. Straight Angle‐is an angle that measures 180°.
C. Complementary and Supplementary angles
1. Complementary Angle—two angles that have a sum of 90°.
2. Supplementary Angle—two angles that have a sum of 180°.
1) Two straight lines that meet at a point form an angle between them.
2)Theorems :
1. If AOB is a straight line,
\(a+b=\)
180°(Adjacent angles on a straight line)2. The sum of all the angles at a point, each being adjacent to the next, is 4 right angles.
(Angles at a point)\(a + b + c + d + e =\)
360°3. If two straight lines intersect, the vertically opposite angles are equal.
(Vertically Opposite angles)\(a=b,c=d\)
4. Parallel lines PQ and RS are cut by a transversal LM, then we have :
The corresponding angles are equal c = b
(Corresponding angles, PQ || RS)The alternate angles are equal a = b
(Alternate angles, PQ || RS)The interior angles are supplementary b + d = 2 right angles
(Interior angles, PQ || RS)To recapLines and angles may seem like basic concepts. However, they are at the foundation of all geometry questions.
Here is an example of how they are applied to a pentagon
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