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Geometry 
Angles 
Parallel Lines 
Triangles 
Quadrilaterials 
– Parallelograms 
Area 
Circles 
Volume
Types of Angles 
• Classification 
– Acute: all angles are less than 90° 
– Obtuse: one angle is greater than 90° 
– Right: has one angle equal to 90° 
• Complementary: the sum of two angles is 90° 
• Supplementary: the sum of two angles is 180° 
• Adjacent: angles that share a side 
• Linear Pair: angles that are both supplementary 
and adjacent
Congruent Angle Pairs 
formed by 
Parallel Lines 
Alternate interior angles 
• <3 & <6, <4 & < 5 
Alternate exterior angles 
• <1 & <8, <2 & <7 
Corresponding angles 
• <1 & <5, <2 & <6, <3 & <7, <4 & <8 
Vertical angles 
• <1 & <4, <2 & <3, <5 & <8, <6 & <7 
1 2 
3 4 
5 6 
7 8
Supplementary Angle Pairs 
Angles that are both on the same side of 
the transversal and either both interior or 
exterior 
• <3 & <5, <4 & < 6, <1 & <7, <2 & < 8 
Linear Pair 
• <1 & <2, <2 & <4, <3 & <4, <1 & <3, 
<5 & <6, <6 & <8, <7 & <8, <5 & <7 
1 2 
3 4 
5 6 
7 8 
formed by 
Parallel Lines
Polygons 
• The sum of the interior angles: (n - 2)(180°) 
• Classified by number of sides (n) 
– Triangle (3) 
– Quadrilateral (4) 
– Pentagon (5) 
– Hexagon (6) 
– Heptagon (7) 
– Octagon (8) 
– Nonagon (9) 
– Decagon (10) 
• Regular Polygon: all sides are congruent
Triangles 
• The sum of the angles in a triangle is 180° 
• a – b < third side < a + b 
• The sum of the two remote interior angles is 
equal to the exterior angles 
• Types: 
Scalene Isosceles Equilateral Right 
Two 
sides are equal One 
Right angle 
All 
sides are equal 
No sides 
are equal
QUADRILATERALS 
PARALLELOGRAM 
Both pairs of opposite 
sides are parallel 
TRAPEZOIDS 
Only one pair of 
Opposite sides parallel 
ISOSCLES 
TRAPEZOID 
A trapezoid that has 
two equal sides 
ROMBUS 
4 equal sides 
RECTANGLE 
4 right angles 
SQUARE 
Both a rhombus 
and a rectangle
Properties of Parallelograms 
Diagonals are 
perpendicular to each other 
Diagonals 
bisect their angles 
Diagonals bisect each other 
Opposite sides are congruent 
Opposite angles are congruent 
Diagonals bisect each other 
Consecutive angles are supplementary 
Diagonals form two congruent triangles 
Diagonals are 
congruent to each other
Area 
½bh bh 
lw 
s2 
½(b1 + b2 )
Circles 
Circumference 
C = 2πr or C = πd 
A = πr2 
• Exact: express in terms of π 
• Approximate: use an approximation of π (3.14)
Volume 
General Formula: V = (area of base)(height) 
1 
3 
1 
3 
e3 
πr2h πr2h 
lwh 
Bh 
4 
πr3 
3

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Geometry 1197608937694019-4

  • 1. Geometry Angles Parallel Lines Triangles Quadrilaterials – Parallelograms Area Circles Volume
  • 2. Types of Angles • Classification – Acute: all angles are less than 90° – Obtuse: one angle is greater than 90° – Right: has one angle equal to 90° • Complementary: the sum of two angles is 90° • Supplementary: the sum of two angles is 180° • Adjacent: angles that share a side • Linear Pair: angles that are both supplementary and adjacent
  • 3. Congruent Angle Pairs formed by Parallel Lines Alternate interior angles • <3 & <6, <4 & < 5 Alternate exterior angles • <1 & <8, <2 & <7 Corresponding angles • <1 & <5, <2 & <6, <3 & <7, <4 & <8 Vertical angles • <1 & <4, <2 & <3, <5 & <8, <6 & <7 1 2 3 4 5 6 7 8
  • 4. Supplementary Angle Pairs Angles that are both on the same side of the transversal and either both interior or exterior • <3 & <5, <4 & < 6, <1 & <7, <2 & < 8 Linear Pair • <1 & <2, <2 & <4, <3 & <4, <1 & <3, <5 & <6, <6 & <8, <7 & <8, <5 & <7 1 2 3 4 5 6 7 8 formed by Parallel Lines
  • 5. Polygons • The sum of the interior angles: (n - 2)(180°) • Classified by number of sides (n) – Triangle (3) – Quadrilateral (4) – Pentagon (5) – Hexagon (6) – Heptagon (7) – Octagon (8) – Nonagon (9) – Decagon (10) • Regular Polygon: all sides are congruent
  • 6. Triangles • The sum of the angles in a triangle is 180° • a – b < third side < a + b • The sum of the two remote interior angles is equal to the exterior angles • Types: Scalene Isosceles Equilateral Right Two sides are equal One Right angle All sides are equal No sides are equal
  • 7. QUADRILATERALS PARALLELOGRAM Both pairs of opposite sides are parallel TRAPEZOIDS Only one pair of Opposite sides parallel ISOSCLES TRAPEZOID A trapezoid that has two equal sides ROMBUS 4 equal sides RECTANGLE 4 right angles SQUARE Both a rhombus and a rectangle
  • 8. Properties of Parallelograms Diagonals are perpendicular to each other Diagonals bisect their angles Diagonals bisect each other Opposite sides are congruent Opposite angles are congruent Diagonals bisect each other Consecutive angles are supplementary Diagonals form two congruent triangles Diagonals are congruent to each other
  • 9. Area ½bh bh lw s2 ½(b1 + b2 )
  • 10. Circles Circumference C = 2πr or C = πd A = πr2 • Exact: express in terms of π • Approximate: use an approximation of π (3.14)
  • 11. Volume General Formula: V = (area of base)(height) 1 3 1 3 e3 πr2h πr2h lwh Bh 4 πr3 3

Editor's Notes

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