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page 2 of 7
1.
Angles and Lines
2. Intersecting Angles
3. Triangles
4. Circles
5. Perimeters
& Areas
6. Solids
7. Coordinate
Geometry
Intersecting Angles
When two lines intersect, they form four angles: angles next to each other are supplementary angles, and angles opposite each other are vertical angles. Vertical angles are equal to each other. Adjacent angles have the same vertex and a common side. Note that in the following diagram angles 1 and 4, 2 and 4, 2 and 3, and 1 and 3 are adjacent angles.
Two parallel lines never intersect. If a third line, a transversal, intersects two parallel lines, eight angles are formed. Corresponding angles are equal: 1 and 5, 2 and 6, 3 and 7, and 4 and 8. Alternate interior angles are equal: 3 and 6, and 4 and 5. The symbol || means "is parallel to."
Two lines that intersect
such that all four angles are equal are perpendicular, and all
four angles are right angles. A small box in a corner indicates
an angle of 90
, a right angle.
The symbol 
means "is perpendicular to":
mn.
m
Example 1
If the complement of an angle is one quarter of its supplement, what is the angle?
Solution
Let x be the angle.
Its complement y is y = 90 - x
Its supplement z is z = 180-xIf y = z/4, we have 90 - x = (180 - x)/4
multiply both sides by 4. 360 - 4x = 180 - x
180 = 3x, x = 60
