Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Technical drawing wikipedia , lookup
Golden ratio wikipedia , lookup
Multilateration wikipedia , lookup
Perceived visual angle wikipedia , lookup
Euler angles wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Incircle and excircles of a triangle wikipedia , lookup
Euclidean geometry wikipedia , lookup
Geometry 5.2 Inside Out 5.2 Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems β’ Objectives β’ Prove the triangle sum theorem β’ Explore the relationship between the interior angle measures and the side lengths of a triangle Yes Can subtract from 180 to find the interior angles (linear pairs) Then all angles inside add to 180 Subtract from 180 to solve for x (linear pair) π₯ = 180 β 128 π₯ = 52π Linear Pair Postulate 52 + 75 + π¦ = 180 π¦ + 127 = 180 π¦ = 53π Problem 1 Triangle Interior Angle Sums #1 Triangle Sum Theorem β’ Draw a triangle on a sheet of paper β’ Tear off the angles β’ Place them next to each other β’ What do you notice about the sum of these angles? β’ βThe sum of the measures of the interior angles of a triangle is 180π .β 1. 2. 3. 4. 5. 6. ππππππππ π΄π΅πΆ π€ππ‘β π΄π΅ β₯ πΆπ· πβ 4 + πβ 3 + πβ 5 = 180π β 1 β β 4, β 2 β β 5 πβ 1 = πβ 4, πβ 2 = πβ 5 πβ 1 + πβ 3 + πβ 2 = 180π πβ 1 + πβ 2 + πβ 3 = 180π 1. 2. 3. 4. 5. 6. πΊππ£ππ π΄ππππ π΄ππππ‘πππ πππ π‘π’πππ‘π π΄ππ‘πππππ‘π πΌππ‘πππππ π΄ππππ πβπ π·ππππππ‘πππ ππ πΆπππππ’πππ‘ π΄πππππ ππ’ππ π‘ππ‘π’π‘πππ πππππππ‘π¦ π΄π π πππππ‘ππ£π πππππππ‘π¦ Problem 2: Analyzing Triangles β’ Collaborate 1, 2, or 3 (5 Minutes) β’ Use Ruler and Protractor β’ Each member of the group will do only one drawing β’ Collaborate 4-6 (3 Minutes) Problem 2: Analyzing Triangles β’ Discuss #7 Together 47π 98π π₯, π§, π¦ π, π, π Start with the small triangle π, π, π πΆπππ‘πππ’π π€ππ‘β π‘βπ πππππ π‘πππππππ π, β, π 95π 112π πΏπππ π‘βπ πππ π‘ π‘ππππ‘βππ π, π, π, β, π Summary β’ What is the sum of all of the angles on the interior of a triangle? β’ The longest side is opposite which angle in a triangle? β’ The smallest angle is opposite which side in a triangle? Formative Assessment β’ Skills Practice 5.2 β’ Pg. 483-485 (1-12)