Geometry Flashcards
Congruent
Equal
Midpoint
The point that divides a line segment into two congruent line segments
Opposite angles are…
congruent, have equal measures
Acute angle
less than 90 degrees
Obtuse angle
more than 90 degrees and less than 180
Z angles with parallel lines are…
equal (4 of 8 equal, other 4 are equal)
perimeter
the sum of the length of the sides
endpoints of a polygon are called…
vertices
if a polygon has n sides, it can be divided into…triangles
n-2
sum of interior angles of a polygon is…
(n-2)(180)
regular polygon
all sides and all interior angles are congruent
Characteristics of an equilateral triangle
all sides are equal
all angles equal 60
Characteristics of an isosceles triangle
two congruent sides (so two opposite equal angles)
third side is 180-2x
Pythagorean theorem
aˆ2 + bˆ2 = cˆ2
where c is the length of the hypotenuse
Lengths of sides in a 45-45-90 triangle
x, x, √2x
Lengths of sides of a 30-60-90 triangle
x, √3x, 2x
Area of a triangle
A = bh / 2
b=base
h=height
What conclusions can be drawn about congruency from the statement: “triangles PQR and STU are congruent”?
PQ and ST are same length
PR and SU are same length
QR and TU are same length
(And corresponding angles are also equal)
Congruent triangles
triangles with the same shape and size
SSS congruence
Side-side-side congruence: if all three sides are congruent, the triangles are congruent
SAS congruence
Side-angle-side congruence: If two sides and the angle between them are congruent, the triangles are congruent
ASA congruence
Angle-side-angle congruence: If two angles and the side between them are congruent, the triangles are congruent
Two ways to prove similar triangles
- corresponding angles are congruent
2. lengths of corresponding sides have same ratio (can set up proportions to calculate)
Congruency in rectangles
- four right angles
- opposite sides are parallel and congruent
- two diagonals are congruent
parallelogram
a quadrilateral in which both pairs of opposite sides are parallel
opposite sides are congruent
opposite angles are congruent
trapezoid
at least one pair of opposite sides is parallel
the parallel sides are the bases
area of a parallelogram (including squares and rectangles)
A = bh
area of a trapezoid
a = 1/2(b1 + b2)(h)
radius
distance from the center to an end
diameter
2r
the distance across the circle going through the middle
chord
any line segment joining two points on the circle
formula for circumference
C = 2πr
arc
the (outer) part of the circle containing two end points and all the points between them
measure of an arc
the measure of its central angle
length of an arc
length of arc / circumference (2πr) is proportionate to the central angle / 360
area of a circle
πrˆ2
area of a sector (piece) of circle
area of sector / area of circle (πrˆ2) is proportionate to central angle / 360
tangent
a line that intersects a circle at exactly one point
a radius drawn to a tangent is …. to the tangent line
perpendicular
If all vertices of a polygon lie on a circle, the polygon is…
and the circle is…
inscribed in the circle
circumscribed about the polygon
If one side of an inscribed triangle is the diameter of the circle, then the triangle is a…
right triangle
volume of a rectangular solid
V = lwh
surface area of a rectangular solid
A = 2(lw + lh + wh)
volume of a right circular cylinder
V = πrˆ2h
right circular cylinder
axis is perpendicular to its bases and the height is a perpendicular distance from both bases
area of a right circular cylinder
A 2(πrˆ2) + 2πrh
common Pythagorean triples
3-4-5 6-8-10 5-12-13 10-24-26 12-16-20 7-24-25
