Need Help In Geometry ? Well , Here Is Your Study Guide

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Need Help In Geometry ? Well , Here Is Your Study Guide by Mind Map: Need Help In Geometry ? Well , Here Is Your Study Guide

1. General Postulates You Should Know

1.1. Segment Addition Postulate - If B is between A and C , the AB + BC = AC

1.2. Angle Addition Postulate - If X is in the interior of <ABC then m <ABX + m <XBC = m <ABC

2. General Theorems You Should Know

2.1. Angle

2.1.1. all right angles are congruent

2.1.2. vertical angles are congruent

2.1.3. if two angles form a linear pair , they are supplementary

2.1.4. exterior angle - the measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles

2.2. Triangle

2.2.1. triangle sum - the sum of the interior angles in a triangle is 180˚

2.2.2. third angle - if two angles of one triangle are congruent to two angles of a second triangle , then the third angles of the triangles are congruent

2.2.3. the base angles in an isosceles triangle are congruent

2.2.4. the sum of the lengths of any two sides of a triangle must be greater than the third side

2.2.5. the longest side is across from the largest angle , the largest angle is across from the longest side

2.2.6. ( isosceles triangle ) if two sides of a triangle are congruent , the angles opposite these sides are congruent

2.2.7. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles

2.3. Parallel Lines

2.3.1. if parallel lines are cut by a transversal , then corresponding angles are congruent

2.3.2. if parallel lines are cut by a transversal , then alternate interior angles are congruent

2.3.3. if parallel lines are cut by a transversal , then alternate exterior angles are congruent

2.3.4. if parallel lines are cut by a transversal , then consecutive interior angles are supplementary

2.3.5. if parallel lines are cut by a transversal , then consecutive exterior angles are supplementary

2.3.6. if corresponding angles are congruent , then the lines are parallel

2.3.7. if alternate interior angles are congruent , then the lines are parallel

2.3.8. if alternate exterior angles are congruent , then the lines are parallel

2.3.9. if consecutive interior angles are supplementary , then the lines are parallel

2.3.10. if consecutive exterior angles are supplementary , then the lines are parallel

3. Definitions

3.1. congruence - two segments are congruent if and only if they have the same measure , two angles are congruent if and only if they have the same measure

3.2. midpoint - a point is a midpoint if and only if it divides a segment into two equal parts

3.3. bisectors

3.3.1. segment bisector - a segment , ray or line is a bisector if and only if it divides a segment into to equal parts

3.3.2. angle bisector - a ray is a bisector if and only if it divides an angle into two equal parts

3.4. perpendicular lines - two lines are perpendicular if and only if they intersect to form a right angle

3.4.1. perpendicular bisector -

3.4.2. * oblique lines are lines that intersect , but do not form a right angle *

3.4.3. skew lines - two lines are skew if and only if they do not intersect and are not in the same plane

3.5. right angle - an angle is a right angle if and only if it measures 90˚

3.6. linear pair - two supplementary adjacent angles whose sides form a line

3.7. angles

3.7.1. complementary angles - a pair of angles whose sum is 90˚

3.7.2. supplementary angles - a pair of angles whose sum is 180˚

3.7.3. adjacent angles - a pair of angles with a shared vertex and common side but do not have overlapping interiors

3.7.4. vertical angles - a pair of angles whose sides form opposite rays

3.8. median - a segment from the vertex of the triangle to the midpoint of the opposite side

3.9. altitude - the perpendicular segment from a vertex of the triangle to the segment that contains the opposite side

3.9.1. in a right triangle - two of the altitudes are the legs of the triangle

3.9.2. in an obtuse triangle - two of the altitudes are outside of the triangle

3.10. segment addition postulate - you must see a point between two other points ( collinear )

4. transveral - a line that intersects two or more lines in a plane at different points