Clil.geometry presentation-

Geometry

Concepts

PointLine RayLine segmentRayAnglesParallel LinesTrianglesQuadrilateralsParallelogramsAreaCirclesVolume

A point can be described as a location in space. Represented by a dot and is named by writing a capital letter next to the dot.

POINT

LINE

A line is a straight row of points that goes on forever in both directions. A line is drawn by using arrow heads at both ends.

A line segment is a piece of a line that has two endpoints. A line segment is named for its endpoints. The segment with endpoints A and B shown to the right is named:

LINE SEGMENT

A ray is a part of a line that has only one endpoint and goes on forever in one direction. A ray is named by using the endpoint and some other point on the ray:

RAY

Lines that are on the same plane, but that never intersect (cross).

PARALLEL LINES

Lines that intersect (cross).

INTERSECTING LINES

Types of Angles

•

Classification–

Acute angle: all angles are less than 90°

–

Obtuse angle: one angle is greater than 90°–

Right angle: has one angle equal to 90°

•

Complementary angle: the sum of two angles is 90°•

Supplementary angle: the sum of two angles is 180°

•

Adjacent angle: angles that share a side

An angle is made up of two rays that start at a common endpoint. The common endpoint is called the vertex. Named:

ANGLE

Angles can be measured in degrees. The symbol for degrees is a small raised circle °

DEGREES

An angle of 180°

is called a straight angle. When two rays go in opposite directions and form a straight line, then the rays form a straight angle

STRAIGHT ANGLE

An angle of 90°

is called a right angle. The rays of a right angle form one corner of a square. So, to show that an angle is a right angle, we draw a small square at the vertex.

RIGHT ANGLE

Acute angles measure less than 90°

ACUTE ANGLE

An Obtuse angle measures more than 90°

but less

than 180°

OBTUSE ANGLE

Two lines are called perpendicular lines if they intersect to form a right angle.

PERPENDICULAR LINES

Two angles are called complementary angles if the sum of their measures is 90°. If two angles are complementary , each angle is the complement of the other.

COMPLEMENTARY ANGLES

Two angles are called supplementary angles if the sum of their measures is 180°

SUPPLEMENTARY ANGLES

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:

Two sides are equal One

Right

angle

All sides are equal

Scalene Isosceles Equilateral Right

No sides are equal

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

Quadrilaterals

PARALLELOGRAM

Both pairs of opposite sides are parallel

TRAPEZOIDS

Only one pair of Opposite sides parallel

ISOSCLESTRAPEZOID

A trapezoid that hastwo equal sides

ROMBUS4 equal sides

RECTANGLE

4 right angles

SQUARE

Both a rhombusand a rectangle

Properties of Parallelograms

Diagonals are perpendicular to each other

Diagonals bisect their angles

Diagonals are perpendicular to each other Diagonals bisect their angles

Diagonals are congruent to each other

Diagonals bisect each otherOpposite sides are congruentOpposite angles are congruentDiagonals bisect each otherConsecutive angles are supplementaryDiagonals form two congruent triangles

Circles

•

Exact: express in terms of π•

Approximate: use an approximation of π

(3.14)

Circumference

C = 2πr or C = πd

A = πr2