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Math 8

Triangles and Transversals

TermDefinition
Angles of a triangle add up to 180 degrees
Straight line 180 degrees
How to find a missing angle INSIDE a triangle x + x + x = 180 30 + 42 + x= 180 72 + x = 180 -72 -72 x = 108 degrees So, add the two known INTERIOR angles and subtract from 180.
How to find a missing angle OUTSIDE a triangle Exterior angle = Remote interior + remote interior x = 30 + 42 x = 72 degrees So, add the two REMOTE INTERIOR angles. DO NOT SUBTRACT FROM 180!!!
Remote interior angle Two interior angles NOT NEXT TO or across from the exterior angle.
Alternate Interior Angles Congruent angles formed by parallel lines cut by a transversal that are both between the parallel lines and on opposite sides of the transversal line.
Alternate Exterior Angles Congruent angles formed by parallel lines cut by a transversal that are both outside the parallel lines and on opposite sides of the transversal line.
Corresponding Angles Congruent angles formed by parallel lines cut by a transversal that are both on the same side of the transversal line but one is between the parallel lines while the other is outside the parallel lines.
Vertical Angles Congruent angles formed by parallel lines cut by a transversal that share a vertex. These are across a vertex from each other and form a "bow tie".
Congruent Angles Angles that are the same degrees.
Complementary Angles Two or more angles that form a right angle (add up to 90 degrees).
Supplementary Angles Two or more angles that form a straight angle (add up to 180 degrees).
Consecutive Interior Angles or Same Side Interior Supplementary angles formed by parallel lines cut by a transversal that are both on the same side of the transversal line and between the parallel lines. One will be acute and one will be obtuse.
Consecutive Exterior Angles or Same Side Interior Supplementary angles formed by parallel lines cut by a transversal that are both on the same side of the transversal line and outside the parallel lines. One will be acute and one will be obtuse.
Adjacent (Linear Pair) Angles Supplementary angles formed by parallel lines cut by a transversal that are next to each other. They will share a vertex and ray. One will be acute and one will be obtuse.
Right Angle 90 degree angle
Acute Angle an angle that is < 90 degrees
Obtuse Angle an angle that is > 90 degrees and < 180 degrees
Straight Angle 180 degree angle
Parallel Lines Lines that run next to each other and never intersect.
Transversal Line Line that crosses two or more parallel lines.
Perpendicular Lines Lines that cross at a 90 degree angle.
How to find a missing supplementary angle Write the equation x + known angle = 180, then subtract the known angle from both sides
How to solve a multistep equation 1. distribute (parentheses- multiply) 2. combine like terms (same side, add) 3. move (+ or -) the variable with the smaller coefficient to get variables on one side 4. move (+ or -) the constant on the side with the remaining variable to get constants on one side 5. multiply or divide by coefficient to get x by itself
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