1. Warm-up 1/5/12 1.Find x, m  1, if m  3 = 3x + 40 and m  4 = 5x + 60. 2. Find the value of x that would make lines m and n parallel. 1 4 3 2 x = 10 3x – 4 + x + 10 = 180 4x + 6 = 180 m  1 = m  3 = 3(10) + 40 m  1 = 70 3x – 4 x + 10 m n t 4x = 174x = 43.5 3x + 40 + 5x + 60 = 180 8x+ 100 = 1808x = 80

2. Classifying Triangles

3. Lesson 3.1B Essential Questions 1.How are triangles classified based on their angle measures and side lengths? 2.Define and draw the median and altitude of a triangle. 3.What are the special characteristics of an isosceles triangle? 4.What is an exterior angle and how do you find the measure of the exterior angle?

4. Standards MM1G1. Students will investigate properties of geometric figures in the coordinate plane. e. Use the coordinate plane to investigate properties of and verify conjecture related to triangles and quadrilaterals

5. Essential Question #1 How are triangles classified based on their angle measures and side lengths?

6. Classification of triangles based on angle measure: Acute Triangle: a triangle with three acute angles Right Triangle: a triangle with two acute angles and one right angle Obtuse Triangle: a triangle with two acute angles and one obtuse angle

7. 1. 2. 3. 37 o 90 o 53 o 44 o 68 o 32 o 116 o 32 o ___________________Triangle _____________________Triangle _________________Triangle Right Acute Obtuse Sum for ∆1:________Sum for ∆2:________ Sum for ∆3:________ 180 o Conjecture: The sum of the interior angles of a triangle is _________ 180 o

8. Using the paper triangle provided by your teacher, tear off the three corners as shown: Now place the three corners together at their tips (called vertices). Make sure that all three corners or angles are placed so they are adjacent. In the space above make a sketch of what these corners look like when they are arranged as adjacent angles. Note they will form a line. Does this support your conjecture above? _______ YES

9. Classifying triangles by the lengths of their edges (sides): Equilateral Triangle – all three sides of the triangle are equal Isosceles Triangle – at least two sides of the triangle are equal. Scalene Triangle – none of the sides of the triangle are equal. 2.2 cm 1.6 cm 3.4 cm 3.7 cm 2.6 cm 3 cm 2.9 cm _________ triangle _________ triangle _________ triangle _________ triangle Equilateral 6.7. 3 cm 2.6 cm 4.8 cm NOTE: If a triangle is equilateral then it is also ________________. Equiangular 4. 5. Scalene IsoscelesScalene

10. .. put our heads together to…. http://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpg Answer Essential Question #1 How are triangles classified based on their angle measures and side lengths?

11. Essential Question #2 Define and draw the median and altitude of a triangle.

12. The ________________________of a triangle is a segment drawn from the vertex perpendicular to the opposite edge. A triangle contains __________________ altitudes. Draw the altitude from point A to the opposite edge. Label the altitude AD. Altitude 3 A AA D D D 8.9.10. In the first triangle, the altitude was drawn on the _______________of the triangle. In the second triangle, the altitude was an _______________of the triangle. In the third triangle, the opposite edge was extended and the altitude was drawn on the ____________________ of the triangle. INSIDE EDGE OUTSIDE

13. The ___________________of a triangle is a segment drawn from the vertex to the midpoint of the opposite edge. A triangle contains _______ medians. Draw the median from point A to the opposite edge. Label the median AM. median 3 A A A M M M 8. 9. 10.

14. .. put our heads together to…. http://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpg Answer Essential Question #2 Define and draw the median and altitude of a triangle.

15. Essential Question #3 What are the special characteristics of an isosceles triangle?

16. Special features of an Isosceles Triangle: Legs: the two congruent edges Base:the edge that is not congruent to the other edges. Vertex Angle : The angle formed by the two congruent edges (its vertex is the point where the congruent sides intersect) Base Angle: The angles formed by a leg and the base (their vertices are the points where the legs intersect the base) Vertex  LEG Base Base 

17. Investigation A: Step 1: Using a straightedge, draw an isosceles triangle on a sheet of patty paper. Label the vertices at the base A and B and the remaining vertex C. Step 2: Fold the triangle so that A and B overlap. Crease the patty paper carefully. Let’s make the following conjectures based on this fold. Base angles of an isosceles triangle are ______________________. The altitude drawn from the vertex angle to the base: (a). _________________ the base. (b). is the same segment as the ___________________. (c). _________________ the vertex angle. Special features of an Equilateral Triangle: If a triangle is equilateral, then it is also _________________________. The measure of each angle in an equilateral triangle is _________ o. All properties of __________________ triangles apply to equilateral triangles. Congruent Bisects Median Equiangular 60 Isosceles

18. .. put our heads together to…. http://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpg Answer Essential Question #3 What are the special characteristics of an isosceles triangle?

19. Essential Question #4 What is an exterior angle and how do you find the measure of the exterior angle?

20. Investigation B: Step 1: Record the measure of  A,  D, and  C from the overhead. Step 2:Extend to the left of the triangle. Label a point on the extension T.  ACT is called an exterior angle. Step 3:Compute: m  ACT = ___________ o Step 4: Compute: m  A + m  D = __________ o  A and  D are called remote interior angles. Conjecture: The exterior angle of a triangle is equal to the __________ of the measures of the two remote interior angles. A C D 90˚ 60˚ 30˚ T 120˚ SUM 120˚

21. .. put our heads together to…. http://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpg Answer Essential Question #4 What is an exterior angle and how do you find the measure of the exterior angle?