geometry guide

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Lines Angles Triangles Quadrilaterals Circles

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LinesAngles

TrianglesQuadrilaterals

Circles

Lines

PointsLine Segments

RaysLines

Intersecting LinesPerpendicular Lines

Parallel LinesSkew Lines

Points

● A point is a precise location in a space. It is labeled with a letter.

Point s

Point t

Point m

Line Segments

● A line that starts at a point and ends at another.

Rays

● A line that starts at one point and keeps on going on the other.

Lines

● A line that keeps on going on both ends.

Intersecting lines

● Intersecting lines are lines that eventually cross at a point.

Perpendicular Lines

● Perpendicular lines are lines that intersect at right angles.

Parallel Lines

● Parallel lines are lines that never cross each other.

Skew Lines

● Skew lines are lines that are not in the same plane.

Angles

AcuteObtuseRight

Vertex/VerticesComplimentarySupplementary

Vertical/OppositeAdjacent

Acute Angle

● An acute angle is an angle that is less than 90 degrees.

Obtuse Angle

● An obtuse angle is an angle that is more than 90 degrees.

Right Angle

● A right angle is an angle that is 90 degrees.

Vertex/Vertices

● A vertex is the middle point of an angle and vertices is the plural for vertex.

Complementary

● Complementary angles are two angles that make a 90 degree angle.

60

30

Supplementary

● Supplementary angles are two angles that make a 180 degree angle.

80100

Vertical/Opposite

● Vertical and opposite are right across from each other.

A B

C D

E

BED andAEC

Are vertical

Adjacent

● Adjacent angles are angles that are side by side and have a common vertex and ray.

M

P

N

Q

R

Triangles

RightObtuseAcute

ScaleneIsosceles

EquilateralSum of Internal Angles

PerimeterAngles

Right Triangles

● Right triangles are triangles that have a right angle.

Obtuse Triangles

● Obtuse triangles are triangles that have an obtuse angle.

Acute triangles

● Acute triangles are triangles that have an acute angle.

Scalene

● Scalene triangles are triangles that have no congruent sides.

Isosceles

● Isosceles triangles are triangles that have two congruent sides.

Equilateral

● Equilateral triangles are triangles that have all equal sides.

Sum of Internal Angles

● When you add up angles and they are 180 degrees.

180 10

Perimeter

● To find the perimeter of a shape you have to add the up all the measurements.

5cm5cm

10cm

10cm

Angles

● Angles are the figures formed by two rays with a common endpoint.

Quadrilaterals

TrapezoidParallelogram

RectangleRhombus

SquareArea of a rectangle

Area of a squareArea of a parallelogram

Area of a trapezoid

Trapezoid

● A shape with one pair of parallel sides.

Parallelogram

● A shape that has two pairs of parallel sides.

Rectangle

● A quadrilateral that had four connected sides and all sides have 90 degree angles.

Rhombus

● A parallelogram that has no congruent sides.

Square

● A shape that has two pairs of parallel sides and congruent sides.

Area of a Rectangle

● To find the area of a rectangle, you have to multiply length times width.

5cm

10cm

Area of a Square

● To find the area of a square, you have to multiply length times width.

10cm

10cm

Area of a Parallelogram

● To find the area of a parallelogram you have to multiply the base times height.

Area of a Trapezoid

● To find the area of a trapezoid you have to multiply the two bases with the height.

Circles

ChordDiameter

ArcRadiusSector

CircumferenceArea of a Circle

Chord

● A line segment with its endpoints on a circle.

Diameter

● A line segment that passes through the middle of a circle and has its endpoints on the edge of the circle.

Arc

● An arc is the distance on the outside edge of a circle.

A

B

AB

Radius

● The distance from the center of a circle to the edge.

Sector

● A piece of the area of a circle.

Circumference

● The distance around a circle (perimeter.) To find the circumference you have to multiply pi (3.14) and the diameter.

6cm

Area of a Circle

● The area of a circle is the space inside it. To find the area you have to multiply pi(3.14) and the radius of the circle squared.

3cm

Other Polygons

HexagonOctagon

Regular polygon

Hexagon

● A figure that has six equal sides.

Octagon

● A figure that has eight equal sides.

Regular polygon

● A polygon that has congruent sides and angles.