Geometry part I

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​Today

​Points

Lines

​Segment

Ray

​Angles

Use Properties of Angles,

Triangles, and the Pythagorean Theoremsegement

​Geometry

​Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is, with arithmetic, one of the oldest branches of mathematics.

​

It is concerned with properties of space that are related with distance, shape, size, and relative position of figures.^[1]

​Point

​a point is a primitive notion that models an exact location in the space and has no length, width, or thickness.

​Line

​In Geometry a line:

• is straight (no bends),

• has no thickness, and

• extends in both directions without end (infinitely).

​Segment

a part of a line that is bounded by two distinct endpoints, and contains every point on the line that is between its endpoints

​Ray

​A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.

​Parallel lines

​In geometry, parallel lines are lines in a point which do not meet; that is, two straight lines in a plane that do not intersect at any point are said to be parallel.

​Intersecting lines

​When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection. 

​Perpendicular lines

​​two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians).

Triangle

​A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle. An angle is formed between two sides. This is one of the important parts of geometry. 

​​Properties of a triangle

These are the properties of a triangle:

1. A triangle has three sides, three angles, and three vertices.

2. The sum of all internal angles of a triangle is always equal to 180

3. The sum of the length of any two sides of a triangle is greater than the length of the third side.

4. The side opposite to the largest angle of a triangle is the largest side.

5. Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

​Pythagorean theorem

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Multiple Choice

What is the correct notation for the figure shown?

• $$\overrightarrow{VW}$$

• $$\overrightarrow{WV}$$

• $$\overline{VW}$$

• $$\overleftarrow{WV}$$

Multiple Choice

Which of the following shows a pair of opposite rays?

Multiple Choice

What is this figure?

• Point

• Line

• Ray

• Line Segment

Multiple Choice

Name this angle

• Acute Angle

• Right Angle

• Obtuse Angle

• Straight Angle

Multiple Choice

What is this figure?

• Point

• Line

• Ray

• Line Segment

Multiple Choice

Name this angle

• acute angle

• right angle

• obtuse angle

• straight angle

Multiple Choice

Name these lines

• Perpendicular Lines

• Parallel Lines

• Intersecting Lines

Multiple Choice

Name this angle

• acute angle

• right angle

• obtuse angle

• straight angle

Multiple Choice

Name these lines

• parallel lines

• perpendicular lines

• intersecting lines

Multiple Choice

Name these set of lines

• Parallel lines

• Perpendicular lines

• Intersecting lines

Multiple Choice

Name this triangle

• acute triangle

• right triangle

• obtuse triangle

• not here

Multiple Choice

Solve for x and find the missing angle.

• 28
• 118
• 180
• 90

Multiple Choice

Solve for x using knowledge about supplementary angles.

• 90
• 61.7
• 180
• 30

Multiple Choice

What type of angle is shown?

• Acute Angle
• Obtuse Angle
• Right Angle
• Straight Angle

Multiple Choice

What is the value of x?

• 40^o
• 65^o
• 180^o
• 55^o

Multiple Choice

If ∢3 is 35^o, what is ∢4?

• 35^o
• 51^o
• 45^o
• 23^o