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8 2 Triangle Sum Theorem
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- Triangle Sum Theorem Focus - Prove the Triangle Sum Theorem
- If you add up the measures of the interior angles of a triangle, What is the total?
- 180º
- How many lines can be drawn through point B that would become parallel to M B
- Unique Parallel line Postulate – Through a point not on a given line, there is one and only one line parallel to the given line. m b This postulate will be used in the proof on the next slide.
- Given: Prove:
- 1. ABC is a triangle
- 2. Draw helping line
- through B so that
- 3.
- 4.
- 5.
- 6.
- 7.
- 1. Given
- 2. Unique Parallel Postulate (pg. 439)
- 3. If the sides of an angle form a straight line, then the angle is a straight angle with a measure of 180º
- 4. Whole-Parts Postulate
- 5. Substitution
- 6. Alternate Interior Angle Theorem
- 7. Substitution Property
- Quadrilateral Theorem
- The sum of the measures of the angles of a quadrilateral are:
- What is the sum of the measures of a rectangle, which is a quadrilateral?
- Theorem: Opposite Angles of Quadrilaterals
- If both pairs of opposite angles of a quadrilateral are equal in measure, …
- then the quadrilateral is a parallelogram.
- What can we find out?
- The ladder is leaning on the ground at a 75º angle. At what angle is the top of the ladder touching the building?
- What can we find out?
- The ladder is leaning on the ground at a 75º angle. At what angle is the top of the ladder touching the building?
- Find the missing angle.
- 47º
- Find the missing angle.
- 47º
- Find the missing angles.
- 120º
- x º
- 55º 25º yº wº
- Exterior Angle Theorem
- An exterior angle of a triangle…
- … is equal in measure to the sum of the measures of its two remote interior angles .
- Find the missing angles’ measurements (L and J).
- 120º
- 55º 25º
- What is the measure of Angle U?
- 120º
- 55º 25º
- In today’s lesson we…
- Proved the Triangle Sum Theorem (180 degrees)
- Found Quadrilaterals’ Interior Angles Theorem to state the total degrees is 360.
- Used the above theorems and the Exterior Angle Theorem to find measurements of a Triangle’s exterior angle.
- Assignment: pg. 443: 2-9, 13
- For Warmup 70° y° z° w° D E 50° x° (x-30)° x° 70° 60° 50° 110° D E 50° 70° (80-30)° 80°
- From tdn.com last night.
- OLYMPIA, Wash. – The state Senate has made good on a promise to help students graduate from high school by passing a bill that would eliminate one diploma obstacle.
- The measure would eliminate the requirement to keep taking the math Washington Assessment of Student Learning every year until graduation.
- High school students who fail the 10th grade math test, would still be required to keep earning math credits, however.
- The bill, which passed on a vote of 43-4, still requires approval in the House. It would affect the class of 2009, if it passes both houses and is signed by the governor.
- The bill is Senate Bill 5498.
- * Legislature (weblink) < http:// www.leg.wa.gov >
- Want to spend class time preparing for math WASL questions?
- Group Work
- Group Points
- Three sections will vote.
- 60% will show favorable response.
- Pg. 446: #17 Proof of Theorem If both pairs of opposite angles of a quadrilateral are equal in measure, then the quadrilateral is a parallelogram.
- Given: JKLM is a quadrilateral Prove: JKLM is a parallelogram
- 1. JKLM is a quadrilateral
- 2.
- 3.
- 4.
- 5.
- 6.
- are supplementary angles
- 8.
- 9.
- 10. are supplementary angles
- 11.
- 12. JKLM is a parallelogram
- 1. Given
- 2. Quadrilateral Sum Theor.
- 3. Given
- 4. Substitution
- 5. Distributive Property
- 6. Division Property of Equality
- 7. Def. of Supplementary angles
- 8. Converse of Co-Interior Th.
- 9. Substitution
- 10. Def. of Supplemental Angles
- 11. Chuck Taylor Co-Interior Th.
- 12. Def. of Parallelogram
- Pg. 447: #34 Proof of Theorem An Exterior Angle of a Triangle is equal in measure to the sum of its two remote interior angles.
- Given: with exterior Prove:
- 1. ABC is a triangle with exterior angle 4.
- 2.
- 3.
- 4.
- 5.
- 6.
- 7.
- 1. Given
- 2. Straight Angle Postulate
- 3. Whole-Parts Postulate
- 4. Substitution
- 5. Triangle Sum Theorem
- 6. Substitution Property
- 7. Subtraction Prop. Of Equality
- Assignment: pg. 444-448: 14-18a, 26-34, 37-40
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