Geometry Review Flashcards
Opposite angles (when two lines intersect)
Are equal, called “congruent angles” or “vertical angles”
Congruent line segments
Line segments that have equal lengths
Polygon with n sides can be divided into
n-2 triangles
Sum of the measures of the interior angles of a polygon
(n-2)(180)
Because there are n-2 triangles in the polygon, and the sum of angles in a triangle is 180*
Regular polygon
All sides are congruent and all interior angles are congruent
The length of each side must be less than…
The sum of the lengths of the two other sides.
Ex. Sides cannot be 4, 7, and 12 because 12 > 4 + 7
Area of triangle
1/2(base)(height)
Triangles are congruent if they have the same
Shape AND size.
3 rules to determine congruency of triangles
All three sides are congruent.
Two sides and their included angle are congruent with that of the other triangle.
Or, one side and two angles are congruent
Similar triangles
Same shape not size.
Angles are congruent.
Area of parallelogram
A = bh
Area of trapezoid (quadrilateral with parallel opposite sides)
A = 1/2 (b1+b2)(height)
Congruent circles
Equal radii
Circumference
C = 2pi(r)
Ratio of arc length to circumference is equal to ratio of…
Arc angle to 360deg
Area of circle
A= pi(r)^2
“Pi r squared”
Sector of circle
Region bound by an arc of the circle and two radii
Ratio of sector area and area of circle is also equal to
Ratio of degree measure to 360 deg.
Tangent line intersects circle…
At ONE point
Polygon is inscribed in a circle if…
All its vertices lie on the circle.
Also described as the circle being circumscribed about the polygon
If one side of an inscribed triangle is a diameter of the circle, then the triangle is…
A right triangle
Polygon can be circumscribed about the circle as well. In order for the circle to be inscribed inside the polygon…
Each side of the polygon must be tangent to the circle (intersect at one point)
Concentric circles
Have the same center
Volume of a rectangular solid
V = lwh
Surface area (rectangular solid)
Sum of the areas of the six faces
2( lw + lh + wh) = A
Circular cylinder
Two congruent circles joined by a lateral surface (made up of all the parallel line segments that join points in the two circles)
Axis (cylinder)
Line segment joining the centers of two circles
Right circular cylinder
Circular cylinder whose axis is perpendicular to its bases
Volume (right circular cylinder)
Area of base x height
V = (pi)r^2h
“Pi r squared times height”
Surface area (right circular cylinder)
Area of each circle plus area of rectangle joining them (2 pi r x height)
A = 2(pi r ^2) + 2 pi r h
