2. PROBLEM 1A PROBLEM 2A PROBLEM 3A PROBLEM 4A PROBLEM 1B PROBLEM 4B PROBLEM 2B PROBLEM 3B TRIANGLES AS POLYGONS: CLASSIFICATION PRESENTATION CREATED BY SIMON PEREZ RHS. All rights reserved Standards 4 and 5 REFLEXIVE, SYMMETRIC AND TRANSITIVE PROPERTIES EXTERIOR ANGLE THEOREM CPCTC ANGLE SUM THEOREM PROBLEM 5APROBLEM 5B

3. STANDARD 4: Students prove basic theorems involving congruence and similarity. ESTÁNDAR 4: Los estudiantes prueban teoremas que involucran congruencia y semejanza. STANDARD 5: Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. ESTÁNDAR 5: Los estudiantes prueban que son triángulos congruentes o semejantes y son capaces de usar el concepto de partes correspondientes de triángulos congruentes.

4. These are examples of POLYGONS: These are NOT POLYGONS: A POLYGON is a closed figure in a plane which is made up of line segments, called sides, that intersect only at their endpoints, named vertices. Standards 4 and 5

5. A TRIANGLE is a three-sided polygon Standards 4 and 5

6. 55° 64°61° 21° 110° 49° RIGHT TRIANGLE ACUTE TRIANGLE OBTUSE TRIANGLE ANGLES CLASSIFYING TRIANGLES BY ANGLES STANDARDS 4 and 5 PRESENTATION CREATED BY SIMON PEREZ RHS. All rights reserved

7. Parts of a RIGHT TRIANGLE Leg HYPOTENUSE Right Angle

8. A A m = 180° B B m + C C m + If and A = 90 ° m then = 180° B m + C m + 90° - 90° -90° = 90° B m C m + Conclusion: In a right triangle, both non- right angles are acute and complementary! What kind of angles are the non-right angles in a right triangle?

9. SIDES CLASSIFYING TRIANGLES BY SIDES 10 4 922 9 13 13 13 SCALENE TRIANGLE ISOSCELES TRIANGLE EQUILATERAL TRIANGLE Standards 4 and 5

10. Sample Questions Identify the triangles by their angles and their sides

11. A C BD Right Triangles Obtuse Triangles Isosceles Triangles Name the type of triangles with the following characteristics

12. 5x 6x-5 3x+10 Find the value of x to make the triangle equilateral.

13. XYZ has coordinates X(2,6) Y(4,-5) Z(-3,0). Classify the triangle by angles and sides.