1 / 22

Lesson 1-4

Angles. Lesson 1-4. Angle and Points. An Angle is a figure formed by two rays with a common endpoint, called the vertex. ray. vertex. ray. Angles can have points in the interior, in the exterior or on the angle. A. E. D. B. C.

anais
Download Presentation

Lesson 1-4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Angles Lesson 1-4 Lesson 1-4: Angles

  2. Angle and Points • An Angle is a figure formed by two rays with a common endpoint, called the vertex. ray vertex ray • Angles can have points in the interior, in the exterior or on the angle. A E D B C Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex. Lesson 1-4: Angles

  3. Naming an angle:(1) Using 3 points (2) Using 1 point (3) Using a number – next slide Using 3 points: vertex must be the middle letter This angle can be named as Using 1 point: using only vertex letter *Use this method is permitted when the vertex point is the vertex of one and only one angle. Since B is the vertex of only this angle, this can also be called . A C B Lesson 1-4: Angles

  4. Naming an Angle - continued Using a number: A number (without a degree symbol) may be used as the label or name of the angle. This number is placed in the interior of the angle near its vertex. The angle to the left can be named as . A B 2 C * The “1 letter” name is unacceptable when … more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present. Lesson 1-4: Angles

  5. Example • K is the vertex of more than one angle. Therefore, there is NO in this diagram. There is Lesson 1-4: Angles

  6. 4 Types of Angles Acute Angle: an angle whose measure is less than 90. Right Angle: an angle whose measure is exactly 90 . Obtuse Angle: an angle whose measure is between 90 and 180. Straight Angle: an angle that is exactly 180 . Lesson 1-4: Angles

  7. Complementary Angles Definition: A pair of angles whose sum is 90˚ Examples: Adjacent Angles ( a common side ) Non-Adjacent Angles Lesson 1-5: Pairs of Angles

  8. Supplementary Angles Definition: A pair of angles whose sum is 180˚ Examples: Adjacent supplementary angles are also called “Linear Pair.” Non-Adjacent Angles Lesson 1-5: Pairs of Angles

  9. Vertical Angles Definition: A pair of angles whose sides form opposite rays. Examples: Vertical angles are non-adjacent angles formed by intersecting lines. Lesson 1-5: Pairs of Angles

  10. Statements Reasons 1. 1. Definition: Linear Pair 2. 2. Property: Substitution 3. 3. Property: Subtraction 4. 4. Definition: Congruence Theorem: Vertical Angles are = ~ Given: The diagram Prove: Lesson 1-5: Pairs of Angles

  11. Adjacent Angles Definition: A pair of angles with a shared vertexand common sidebut do not have overlapping interiors. Examples: 1 and 2 are adjacent. 3 and 4 are not. 1 and ADC are not adjacent. 4 3 Adjacent Angles( a common side ) Non-Adjacent Angles Lesson 1-5: Pairs of Angles

  12. Adding Angles • When you want to add angles, use the notation m1, meaning the measure of 1. • If you add m1 + m2, what is your result? m1 + m2 = 58. m1 + m2 = mADC also. Therefore, mADC = 58. Lesson 1-4: Angles

  13. Angle Addition Postulate Postulate: The sum of the two smaller angles will always equal the measure of the larger angle. Complete: m  ____ + m ____ = m  _____ MRK KRW MRW Lesson 1-4: Angles

  14. Angle Addition Postulate Postulate: The sum of the two smaller angles will always equal the measure of the larger angle. Complete: m  ____ + m ____ = m  _____ MRK KRW MRW Lesson 1-4: Angles

  15. Angle Bisector An angle bisector is a ray in the interior of an angle that splits the angle into two congruent angles. Example: Since 4   6, is an angle bisector. 5 3 Lesson 1-4: Angles

  16. Congruent Angles Definition: If two angles have the same measure, then they are congruent. Congruent angles are marked with the same number of “arcs”. The symbol for congruence is  3 5 Example: 3   5. Lesson 1-4: Angles

  17. Example • Draw your own diagram and answer this question: • If is the angle bisector of PMY and mPML = 87, then find: • mPMY = _______ • mLMY = _______ Lesson 1-4: Angles

  18. What’s “Important” in Geometry? 4 things to always look for ! 90˚ 180˚ 360˚ Most of the rules (theorems) and vocabulary of Geometry are based on these 4 things. . . . andCongruence Lesson 1-5: Pairs of Angles

  19. Example:If m4 = 67º, find the measures of all other angles. Step 1: Mark the figure with given info. Step 2: Write an equation. 67º Lesson 1-5: Pairs of Angles

  20. Example: Ifm1 = 23 º and m2 = 32 º, find the measures of all other angles. Answers: Lesson 1-5: Pairs of Angles

  21. Example: If m1 = 44º, m7 = 65º find the measures of all other angles. Answers: Lesson 1-5: Pairs of Angles

  22. Algebra and Geometry Common Algebraic Equations used in Geometry: ( ) = ( ) ( ) + ( ) = ( ) ( ) + ( ) = 90˚ ( ) + ( ) = 180˚ If the problem you’re working on has a variable (x), then consider using one of these equations. Lesson 1-5: Pairs of Angles

More Related