Theorem 9.1:[Alternate Interior Angle Theorem] If two lines cut by a transversal have a pair of congruent alternate interior angles, then the two lines are non-intersecting.
_\_________ .a\b _c\d________ .....\ When a line crosses 2 lines, 8 angles are formed. Four are exterior angles - outside the 2 lines, and four are interior angles. These are labelled a, b, c, d in the diagram. a & d are alternate interior angles because they alternate from one side of the intersecting line to the other; b & c are also alternate interior angles. They are also known as "Z-angles" because the top parallel line, the transversal and the bottom parallel line which define the two angles for the letter Z (or a distorted version of it). If angle a = angle d (in which case angle b = angle c as well), the 2 lines drawn horizontally are parallel. If alternate interior angles are equal, the 2 lines are parallel. OR If you know the lines are parallel, then alternate interior angles must be equal. Not the greatest diagram; please ignore the ... but even a lousy diagram helps. And no, you don't use lower case letters for angles but there shouldn't be any confusion.
converse of the angle bisector theorem
According to Lami's theorem, if a particle under the simultaneous action of three forces is in equilibrium, then each force has a constant ratio with the sine of the angle between the other two forces.
The angle of the resultant force can be calculated using trigonometry principles such as the Pythagorean theorem and inverse trigonometric functions. Given the magnitudes of the two component forces, you can determine the angle using the formula: angle = arctan(opposite/adjacent). This will help you find the direction in which the resultant force is acting.
Exterior angles are the angles formed when a side of a polygon is extended, and they are adjacent to the interior angle at that vertex. In a polygon with n sides, there are n exterior angles, one at each vertex. The sum of the exterior angles of any polygon is always 360 degrees.
Pair of Alternate Interior angle are Congruent
GEF is the alternate interior angle of angle hge.
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exterior angle theorem
Pairs of Alternate Exterior Angle are Congruent
Both alternate interior and alternate exterior angle pairs lie on opposite sides of the transversal.
angle 3 and 5
Alternate int angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal
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An exterior angle of a triangle is equal in measure to the sum of the other two interior angles.
An interior angle is an angle defined by two sides of a polygon and that is inside the polygon. Opposite interior angles are specific pairs of interior angles, those that are opposite each other in the polygon. Alternate or opposite interior angles are also angles that lie on opposte sides of the tranversal line that cuts through parallel lines.
360 divided (180-n) This uses the exterior angle theorem and linear pair theorem. This works on regular polygons. All the angles congruent.