the mathematical study of the properties, measurements, and relationships of points, lines, planes,...
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The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids.
Geometry
Lines of Symmetry
• A line that divides a figure into two halves that are reflections of each other.
Transformations
• Reflection
• Rotation
• Translation
Two-Dimensional Figures
Polygons
•A simple closed figure formed by 3 or more sides.
•The number of sides determines the name of the polygon.
Regular Polygons
•A regular polygon is a polygon with all sides congruent and all angles congruent.
Triangles
•A polygon with 3 sides and 3 angles.
•Triangles can be classified by the length of their sides.
•Triangles can be classified by the kind of angles.
TrianglesClassified by their sides
•Equilateral Triangle
-all 3 sides equal in length
-all 3 angles equal in measure
TrianglesClassified by their sides
•Isosceles Triangle
-2 sides are congruent
-the two angles opposite the congruent sides, angles K and L, are the base angles
-the base angles are congruent
K L
M
TrianglesClassified by their sides
•Scalene Triangle
-0 sides equal in length
TrianglesClassified by their angles
•Acute Triangle
-all 3 angles acute
60°
60° 60°
The sum of the angles in a triangle equals 180°.
TrianglesClassified by their angles
•Obtuse Triangle
-1 obtuse angle
-2 acute angles
The sum of the angles in a triangle equals 180°.
120° 35°
25°
TrianglesClassified by their angles
•Right Triangle
-1 right (90°) angle
-2 acute angles
90°
60°
30°
The sum of the angles in a triangle equals 180°.
Quadrilaterals• A polygon with
4 sides.• Some special
quadrilaterals include:
• Square• Rectangle• Parallelogram• Rhombus• Trapezoid
Square
• 4 right (90°) angles
• Opposite sides parallel
• All sides equal in length
90°90°
90° 90°
• The sum of the angles equals 360°.
90°+ 90° + 90° + 90° = 360°
90° x 4 = 360°
Rectangle
• 4 right (90°) angles
• Opposite sides parallel
• Opposite sides equal in length
90°90°
90° 90°
• The sum of the angles equals 360°.
90°+ 90° + 90° + 90° = 360°
90° x 4 = 360°
Rhombus
• Opposite sides parallel
• All sides equal in length
• The sum of the angles equals 360°.
80°+ 80° + 100° + 100° = 360°
80°
80° 100°
100°
Parallelogram
•Opposite sides parallel
•The sum of the angles equals 360°.
80°+ 80° + 100° + 100° = 360°
80°
80° 100°
100°
Trapezoid
•Has one pair of parallel sides
•The sum of the angles equal 360°.
80°+ 80° + 100° + 100° = 360°
100°100°
80°80°
Compare a rectangle and a parallelogram.
Are alike because:• opposite sides
parallel• opposite sides congruent
• four sides
Are different because:• rectangles have
four right angles
Find the missing angle measurement in the
quadrilateral.
80°
100° 100°
1 = ____ 80°
1
Find the missing angle measurement in the triangle.
90°
60° 1 = ____ 30°
1
Find the missing angle measurement in the
quadrilateral.
90°
90° 80° 1 = ____ 100°
1
Find the missing angle measurement in the triangle.
78° 78°
1 1 = ____ 24°