Today we will be learning about Good Afternoon! Today we will be learning about Angles (right, acute, obtuse) protractor Let’s warm up : Classify each pair of lines as parallel, intersecting, or perpendicular. 1 2 1) parallel 2) intersecting 3 4 4) parallel 3) perpendicular CONFIDENTIAL

Let’s review what we did in the last session Parallel lines Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. l m Lines m and l are parallel lines. They will travel to infinity in either direction and never intersect. CONFIDENTIAL

Lines can only intersect at one point and only one point. Review Intersecting lines Two or more lines that meet at a point are called intersecting lines. That point would be on each of these lines. x Q y In the Figure, lines x and y are intersecting lines and intersect at point Q. Lines can only intersect at one point and only one point. CONFIDENTIAL

Review Perpendicular lines. If the line segments meet or cross each other to form square corners, they are perpendicular to each other. s right angles t The little box drawn in the corner, means "at right angles“. Perpendicular lines intersect at a point and form 4 right angles. CONFIDENTIAL

What is the difference between perpendicular and parallel? Review What is the difference between perpendicular and parallel? 90 degrees (a right angle) If you rotate a perpendicular line by 90° it will become parallel (but not if it touches!), and the other way around. perpendicular lines rotate parallel CONFIDENTIAL

Symbols in Geometry || Here are the some geometrical symbols: Symbol Review Symbols in Geometry Here are the some geometrical symbols: Symbol Meaning Example In Words || parallel EF||GH The line EF is parallel to line GH perpendicular AB CD The line AB is perpendicular to line CD Right angle is 90° A right angle is 90 degrees CONFIDENTIAL

Angles (right, acute, obtuse) protractor Let’s start with Angles (right, acute, obtuse) protractor What Is an Angle? An angle is a combination of two rays with a common endpoint. B angle AOB vertex O A arm The endpoint (O) is known as the vertex of the angle And the rays (OA and OB) are called the sides or arms of the angle . CONFIDENTIAL

Labeling Angles There are two main ways to label angles: A 1) By giving the angle a name, usually a lower-case letter like a or b, or sometimes a Greek letter like α (alpha) or θ (theta). a C B θ 2) Or by the three letters on the shape that define the angle, with the middle letter being where the angle actually is (its vertex). D Here, angle "a" is "BAC", and angle "θ" is "BCD" CONFIDENTIAL

We use a little circle ° following the number to mean degrees. Measurement of Angles We use a little circle ° following the number to mean degrees. For example: 45° means 45 degrees. There are 360 degrees in one Full Rotation (one complete circle around). Half a circle is 180°. Quarter of a circle is 90° . CONFIDENTIAL

Measuring angles in Degrees We often measure degrees using a protractor. The normal protractor measures 0° to 180°. CONFIDENTIAL

Types of Angles As the angle increases, the name of the angle Changes. The angle classification is summarized as follows: Type of Angle Description Acute angle An angle that is less than 90° Right angle An angle that is 90° exactly Obtuse angle An angle that is greater than 90° but less than 180° Straight angle An angle that is 180° exactly Reflex angle An angle that is greater than 180° CONFIDENTIAL

Angles On a Straight Line Angles on one side of a straight line will always add to 180 degrees. If a line is split into 2 and you know one angle you can always find the other one. CONFIDENTIAL

If we know one angle is 45°, what is angle “x" ? Angle x will be 180° − 45° = 135° This method can be used to find angles on one side of a straight line. CONFIDENTIAL

Angles around a point will always add up to 360 degrees. 110° 40° 60° 150° The angles here all add to 360°. 40° + 110° + 150° + 60° = 360° Because of this, if there is an unknown angle we can always find it. CONFIDENTIAL

But the angles don't have to be together to Complement each other. Complementary Angles Two Angles are Complementary if they add up to 90 degrees (a Right Angle). 60° 30° These two angles (40° and 50°) are Complementary Angles, because they add up to 90°. But the angles don't have to be together to Complement each other. CONFIDENTIAL

But the angles don't have to be together to Supplement each other. Supplementary Angles Two Angles are Supplementary if they add up to 180 degrees (a Straight Angle). 120° 60° These two angles (120° and 60°) are Supplementary Angles, because they add up to 180°. But the angles don't have to be together to Supplement each other. CONFIDENTIAL

BREAK CONFIDENTIAL

Click on the link below for some exciting puzzle GAME Click on the link below for some exciting puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw-puzzles/12-piece-jigsaw/121805snogirl.html CONFIDENTIAL

Find the missing angle: Assignments Find the missing angle: ? 1 55° 2 40° ? 1) 35° 60° 2) 110° 150° 3 130° ? 3) 50° CONFIDENTIAL

Find the Complement of the following: 4 ? 5 61° 25° ? 4) 65° 5) 29° 6 ? 27° 6) 63° CONFIDENTIAL

Find the Supplement of the following: 7 8 125° 110° ? ? 8) 70° 7) 55° 9 9) 135° ? 45° CONFIDENTIAL

Find the missing angle around a point: 10) 160° 10) 30° + 110° + a° + 60° = 360° 11) 140° 11) 45° + 105° + a° + 70° = 360° 12) 105° 12) 50° + 130° + 75° + a ° = 360° CONFIDENTIAL

Very Good! Let's Review What Is an Angle? An angle is a combination of two rays with a common endpoint. B angle AOB vertex O A arm The endpoint (O) is known as the vertex of the angle And the rays (OA and OB) are called the sides or arms of the angle . CONFIDENTIAL

Measuring angles in Degrees Review Measuring angles in Degrees We often measure degrees using a protractor. The normal protractor measures 0° to 180°. CONFIDENTIAL

Angles On a Straight Line Review Angles On a Straight Line If we know one angle is 45°, what is angle “x" ? x 45° Angle x will be 180° − 45° = 135° This method can be used to find angles on one side of a straight line. CONFIDENTIAL

Angles around a point will always add up to 360 degrees. Review Angles Around a Point Angles around a point will always add up to 360 degrees. 110° 40° 60° 150° The angles here all add to 360°. 40° + 110° + 150° + 60° = 360° Because of this, if there is an unknown angle we can always find it. CONFIDENTIAL

But the angles don't have to be together to Complement each other. Review Complementary Angles Two Angles are Complementary if they add up to 90 degrees (a Right Angle). 60° 30° These two angles (40° and 50°) are Complementary Angles, because they add up to 90°. But the angles don't have to be together to Complement each other. CONFIDENTIAL

But the angles don't have to be together to Supplement each other. Review Supplementary Angles Two Angles are Supplementary if they add up to 180 degrees (a Straight Angle). 120° 60° These two angles (120° and 60°) are Supplementary Angles, because they add up to 180°. But the angles don't have to be together to Supplement each other. CONFIDENTIAL

See you in the next session. You have done a nice job. See you in the next session. CONFIDENTIAL