+ Do Now Take out your compass and a protractor. Look at the new seating chart and find your new seat. Classify this triangle: By angles By side lengths On a piece of paper draw a triangle. (It can be acute, right, or obtuse.) Make it big enough to measure the angles.

+ Isosceles Triangles

+ TODAY’S OBJECTIVES Discover the relationship between the base angles of an isosceles triangle. Explain the sum of the measures of the angles of a triangle. Write a paragraph proof. Use problem solving skills.

+ YOU MAY ASSUME THAT… Lines are straight If two lines intersect, they intersect at a point.

+ DO NOT ASSUME THAT… Lines are parallel unless they are marked parallel, even if they “look” parallel Lines are perpendicular unless they are marked perpendicular, even if they “look” perpendicular Pairs of angles, segments, or polygons are congruent unless they are marked congruent, even if they “look” congruent.

+ The triangle sum: Investigation On a piece of paper, draw a triangle. (Make sure your group has at least one obtuse and one acute triangle.) Measure all three angles as accurately as possible. Find the sum of the measures of the three angles. Compare with your group. Mark your angles A, B, and C. Cut out the triangle. Tear off the three angles. Arrange them so their vertices meet at a point. How does this arrangement show the sum of the angle measures?

+ Triangle Sum Conjecture The sum of the measures of the angles in every triangle is___. 180 o. Based on what type of reasoning? Inductive. Can we prove it using deductive reasoning? Let’s prove it!

+ Proof of Triangle Sum Conjecture As a group, explain why the Triangle Sum Conjecture is true by writing a paragraph proof (a deductive argument that uses written sentences to support its claims with reasons). Hints to get started: What are you trying to prove? How are the angles related? Mark your diagram. How can you use the information you have to prove that the Triangle Sum Conjecture is true for every triangle? Remember what you can and cannot assume.

+ Practice Solve for p and q.

+ Properties of Isosceles Triangles Two sides are congruent

+ Base Angles in an Isosceles Triangle: Investigation 1. Draw an angle. Label it  C. This will be the vertex angle of your isosceles triangle. 2. Place a point A on one ray. Using your compass, copy segment CA onto the other ray and mark point B so that CA=CB. 3. Draw AB. How do you know Δ ABC is isosceles? Name the base and the base angles. Use your protractor to measure the base angles. What do you notice?

+ Isosceles Triangle Conjecture If a triangle is isosceles, then ____________________________. it’s base angles are congruent. Is the converse true? Let’s find out.

+ Converse: Investigation Draw a segment and label it AB. Draw an acute angle at A. Copy  A at point B on the same side of the segment. Label the intersection of the two rays point C. Use your compass to compare the lengths of AC and BC. What do you notice?

+ Converse of the Isosceles Triangle Conjecture If a triangle has two congruent angles, then _______________. it is an isosceles triangle.

+ Practice Find the measure of  T.

+ Stations Collaborative: Start your group project. Independent: Get familiar with McGraw Hill Direct: Practice.

+ What’s wrong with this picture? A

+ Practice Solve for r, s and t.

+ Practice The perimeter of Δ QRS is 344. m  Q= QR=

+ TODAY’S OBJECTIVES Discover the relationship between the base angles of an isosceles triangle. Explain the sum of the measures of the angles of a triangle. Write a paragraph proof. Use problem solving skills.

+ Exit Slip For each question, show your work and explain your reasoning. 1. Find x (above). 2. m  A= 3. a= 4. The perimeter of Δ ABC=

+ Honors Exit Slip 1. Find x (above). Explain your reasoning. 2. m  A= 3. The perimeter of Δ ABC= 4. Use the diagram below to explain why Δ PQR is isosceles.