By Vinny Crandle.  Adjacent Angles- two angles that are coplanar and the same vertex and a side in common, but no common interior points.   Linear.

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Presentation transcript:

By Vinny Crandle

 Adjacent Angles- two angles that are coplanar and the same vertex and a side in common, but no common interior points.   Linear Pair- two adjacent angles with noncommon sides that are opposite rays. 

 Vertical Angles- two angles that are not adjacent and are formed by two intersecting lines. 1 4  2 3 Examples: ∠ 1 and ∠ 3 ; ∠ 2 and ∠ 4

 Vertical angles are congruent.  Complementary angles are two angles with the sum of ninety degrees.   Supplementary angles are two angles with the sum of one hundred eighty degrees.   Angles in a linear pair are supplementary.

 Perpendicular lines form right angles when they intersect.  ⟘ is the symbol for perpendicular lines.

 What should be assumed: 1. Straight lines and angles 2. Collinearity of points 3. Betweeness of points 4. Relative positions of points  What should not be assumed: 1. Right angles 2. congruent segments 3. Congruent angles 4. Relative sizes of segments and angles

 Find the value of each variable. (3x + 20)  80  Set the angles equal to each other because they vertical angles. 3x+20=80 3x=60 x=20

(3x)  (4x+131)  Add both angles to 180 because they are supplementary. 3x+4x+131=180 7x+131=180 7x=49 x=7

Solve for y when the perimeter is y 2y 2y 4y 2(4y)+2(2y)=156 8y+4y=156 12y=156 y=13

Find m ∠1, m∠2, and m∠3 if ∠1=7x, ∠2=2x, and ∠3=x x+2x+x=180 10x=180 x=18 m∠1=7(18) m∠1=126  m∠2=2(18) m∠2=36  m∠3=18 

Carter, John A. Geometry. Bothell, WA: McGraw-Hill, Print. Mr.Pricci’s Honors Geometry Tools of Geometry Sections