Geometry Formulas and Classifications
This content covers various geometry topics such as classifying polygons, determining side lengths, identifying shapes using slope formulas, and more. Detailed explanations, formulas, and calculations are provided along with visual aids for better understanding.
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CP Geometry Mr. Gallo
Classifying Polygons in the Coordinate Use three formulas: Formula When to Use it Distance Formula To determine whether: Sides are congruent Diagonals are congruent ( ) ( ) 2 2 = + d x x y y 2 1 2 1 Midpoint Formula To determine: Coordinates of midpoint of side Whether diagonals bisect each other ( ) ( , ) + + x x y y = 1 2 1 2 M 2 2 To determine whether: Opposite sides are parallel Diagonals are perpendicular Sides are perpendicular Slope Formula y x y x = m 2 1 2 1
Is ??? scalene, isosceles or equilateral? Use the distance formula to find the side lengths: 6 ( ) ( ) 2 2 RS = 3 4 + + 3 1 4 S 7.28 = 53 RS = + 2 2 7 2 2 R ( ) ( ) 2 2 ST = 3 1 + 3 3 + -5 5 6.32 = 40 ST = + 2 2 2 6 -2 ( ) ( ) 2 2 RT = 1 4 + + ) 4 = 3 1 T -4 ( 2 6.4 RT = + 2 5 41 -6 ??? is a scalene triangle
Is parallelogram ACBD a rhombus? Explain. Use the slope formula to find the slopes of the diagonals: 6 + 3 5 2 4 8 4 3 4 = = = of m CD C 6 B 2 + 2 4 5 3 + 6 8 3 4 = = = of m AB -5 5 -2 3 4 4 3 Product of slopes: = 1 -4 A D -6 It is a rhombus
What is the most precise classification of the quadrilateral formed by connecting the midpoints of the sides of the isosceles trapezoid? Use the midpoint formula to find the midpoints of the sides: 6 ( ) ( , ) 3 4 2 3 2 2 = of M OL 4 (0,3) O ( N P ) OL = of 3.5,0.5 M 2 (3.5,0.5) (-3.5,0.5) Q S ( ) ( , ) + 3 4 2 3 2 2 = of M NM -5 5 ( R ) -2 L M = of NM 3.5,0.5 M (0,-2) ( ( ) -4 = 0, 2 of LM M ) = of NM 0,3 M -6
Use the distance formula to find the side lengths: ( ) ( 0 3.5 2 0.5 RS = + + ) ( ) ( ) 2 2 2 2 4.3 4.3 RQ = + + 3.5 0 0.5 2 ( ) ( ) 2 2 4.3 SP = 0 3.5 + + 3 0.5 6 ( ) ( ) 2 2 4.3 PQ = 0 3.5 + 3 0.5 4 Find the slopes of the sides: (0,3) O N P + 0.5 2 3.5 0 0.5 2 3.5 0 2 = of m RS .714 (3.5,0.5) (-3.5,0.5) Q S + -5 5 = of m RQ .714 R -2 L M (0,-2) Product of slopes: ( ) .714 .714 .51 -4 It is a rhombus -6
Complete Got It? #1, 2 & 3 p.401-402 Scalene 1. 2. Yes, ????? ?? ?? = ????? ?? ?? = 3 and ????? ?? ?? = ????? ?? ?? = 1 3 10 b. Yes; ?? = ?? = ?? = ?? = Yes; ????? ?? ?? =3 Therefore, ? is a right angle and ??? is a right triangle. 3. Rhombus 4 and ????? ?? ?? = 4 3. c. Side length is 13 a.
