Classifying Triangles Using Pythagorean Theorem

1. Classifying Triangles Using Pythagorean Theorem Samantha Louis

2. Intro. • You can classify a triangle by their angle measures using the Pythagorean Theorem. • The Pythagorean Theorem can help classify a triangle as obtuse, acute, or right. • C² = A² + B² is the Pythagorean Theorem formula.

3. Formula. • C² = A² + B² • To use this formula, plug in the length of the 2 legs of the triangle into A and B and the hypotenuse into C. • If C² is greater than (>) A² + B² than the triangle is classified as obtuse. • If C² is less than (<) A² + B² than the triangle is classified acute. • If C² is equal to (=) A²+ B² than the triangle is classified as right.

4. Example. • C² = A² + B² • 15² = 9² + 13² • 225 = 81 + 169 • 225 < 250 • The triangle is classified as acute because 225 is less than 250. 15 13 9

5. Example. • C² = A² + B² • 12² = 9² + 4² • 144 = 81 + 16 • 144 > 97 • The triangle is classified as obtuse because 144 is greater than 97. 12 9 4

6. Example. • C² = A² + B² • 10² = 8² + 6² • 100 = 100 • The triangle is classified as right because 100 equal to 100. 10 6 8

8. Helpful Websites • http://www.education.com/reference/article/classifying-triangles/ • http://www.cliffsnotes.com/study_guide/Extension-to-the-Pythagorean-Theorem.topicArticleId-18851,articleId-18820.html • http://www.tutorvista.com/bow/classify-triangles-learning

9. Converse Consecutive Angle Theorem Definition: Two angles that are on opposite sides of the transversal outside of the lines it intersects. If the 2 two lines are parallel these angles are supplementary. This theorem stems from corresponding angle postulate.

10. Rules, Properties and Formulas • If consecutive angles are supplementary then the lines are parallel

11. Examples Name all consecutive angle pairs

12. Sites: • http://www.waterfordmgmt.com/school/Prepared_Notes/parallel_line_geometry.pdf • http://quizlet.com/726842/geometry-chapter-3-vocab-thanks-to-katie-flash-cards • http://www.cliffsnotes.com/study_guide/Testing-for-Parallel-Lines.topicArticleId-18851,articleId-18780.html

13. Triangle Classification by Sides and Angles This goal of this slideshow is to show you all of the possible ways to classify triangles by their sides or angles. You can classify a triangle by its sides by calling it an isosceles triangle, a scalene triangle, or an equilateral triangle. You can classify a triangle by its angles by calling it an equiangular triangle, a right triangle, an acute triangle, or an obtuse triangle. The angle classification always goes before the side classification. Summary Lili Feinberg

14. Rules Equilateral Triangle: A triangle with all three sides equal in measure. Isosceles Triangle: A triangle in which at least two sides have equal measure. Scalene Triangle: A triangle where all three sides are different Measures. Right Triangle: A triangle that has a right angle in its interior. Acute Triangle: A triangle with all acute angles in its interior (less than 90 degrees). Obtuse Triangle: A triangle with an obtuse angle in its interior (less than 180 degrees, but more than 90 degrees). Equiangular Triangle: A triangle having all angles of equal Measure.

15. Examples Classify the triangles by their sides and angles. Click the space bar to reveal the answers so you can check them. Equiangular Equilateral Right Isosceles Acute Scalene

16. Converse Corresponding Angles Postulate By Katie Ostuni

17. Definition • The Converse Corresponding Angle Postulate is if two lines are cut by a transversal so that corresponding angles are congruent, then two lines are parallel.

18. Rules, Properties, and important information. • The converse corresponding angles postulate says that if two lines are cut by a transversal so that corresponding angles are congruent then two lines are parallel. • A converse is a situation, object or statement that is the reverse of another. • The Converse came from the corresponding angles postulate which says if two parallel lines are cut by a transversal then corresponding angles are congruent.

19. Examples Are these lines parallel ? Answer: yes they are because of the converse corresponding angles postulate.

20. Examples (Cont.) • Is this an example of the Converse Corresponding Angles Postulate? • Answer: no, this is an example of the converse alternate interior angles postulate.

21. Web Pages • http://hotmath.com/hotmath_help/topics/corresponding-angles-postulate.html • http://www.regentsprep.org/regents/math/geometry/GPB/theorems.htm • http://www.regentsprep.org/regents/math/geometry/GPB/theorems.htm