1. ADVANCED GEOMETRY 3.6 Types of Triangles LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications.

2. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications. Given: Prove: A B C D E F Warm-Up

3. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications. There are two ways to classify triangles, by sides and by angles. Classify by Sides: Definition If a triangle is a SCALENE TRIANGLE, then no two sides are congruent. If no two sides of a triangle are congruent, then the triangle is a SCALENE TRIANGLE.

4. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications. Classify by Sides (cont.): Definition If a triangle is an ISOSCELES TRIANGLE, then at least two sides are congruent. If at least two sides of a triangle are congruent, then the triangle is an ISOSCELES TRIANGLE. leg base vertex angle base angles Definition If a triangle is an EQUILATERAL TRIANGLE, then all of its sides are congruent. If all sides of a triangle are congruent, then the triangle is an EQUILATERAL TRIANGLE.

5. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications. Classify by Angles: Definition If a triangle is an ACUTE TRIANGLE, then ALL of its angles are acute. If ALL angles of a triangle are acute, then the triangle is an ACUTE TRIANGLE. Definition If a triangle is an EQUIANGULAR TRIANGLE, then ALL of its angles are congruent. If ALL angles of a triangle are congruent, then the triangle is an EQUIANGULAR TRIANGLE.

6. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications. Classify by Angles (cont.): Definition If a triangle is a RIGHT TRIANGLE, then ONE of its angles is a right angle. If ONE angles of a triangle is a right angle, then the triangle is a RIGHT TRIANGLE. Definition If a triangle is an OBTUSE TRIANGLE, then ONE of its angles is obtuse. If ONE angle of a triangle is obtuse, then the triangle is an OBTUSE TRIANGLE. Hypotenuse leg

7. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications. Is a triangle that is equilateral also isosceles? Is a triangle that is isosceles also equilateral? How many total degrees are there in the three angles of any triangle? How many degrees are in each angle of an equiangular triangle? Can a triangle have two right angles? Explain. Why can there only be one obtuse angle in a triangle?

8. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications. Is an equiangular triangle an equilateral triangle? Could a triangle be both obtuse and isosceles? Could a triangle be both right and isosceles? Could a triangle be both obtuse and equilateral? Could a triangle be both right and equilateral? Is an equiangular triangle a scalene triangle? Is an equiangular triangle an acute triangle?

9. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications.

10. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications.

11. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications. Statement Reason

12. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications. HW: Pg. 144 # 1, 5, 9, 10, 11, 16

13. LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs using these classifications.