1. Warm-Up Given: AB has endpoints A (3, -4) and B (-1, -6) Find: Midpoint M and Distance

2. Use the Distance Formula Triangle Side Length Classification

3. Classifying Triangles by Sides Scalene No Sides Congruent Isosceles 2 Congruent Sides Equilateral 3 Congruent Sides

4. Classifying Triangles by Angles Acute 3 Acute Angles Right 1 Right Angle Obtuse 1 Obtuse Angle Equiangular 3 Congruent Angles

5. Example 1 Classify the triangles by its sides and angles. A Right Scalene Triangle 70◦ C D Acute Isosceles Triangle Z Y X A B C Equilateral Equiangular Triangle

6. Example 2 A triangle has the given vertices. Graph the triangle and classify by its sides. C B A Step 1: Use the distance formula to find the length of AC. A(1, 3), B(5, 3) C(3, 6)

7. Example 2 A triangle has the given vertices. Graph the triangle and classify by its sides. C B A Step 2: Use the distance formula to find the length of CB. A(1, 3), B(5, 3) C(3, 6)

8. Example 2 A triangle has the given vertices. Graph the triangle and classify by its sides. C B A Step 3: Use the distance formula to find the length of AB. A(1, 3), B(5, 3) C(3, 6) AB = 4 Step 4: What is the classification of the triangle? Isosceles

9. Example 3 The center of a circle is C (4, -2) and the point P (-3, 8) is on the circle. Find the radius of the circle. Step 1: Use the distance formula to find the length of CP. CP ≈ 12.207

10. Example 4 The circle has a center of (-3, -5) and a radius of 6. Determine whether the given point is on the circle, inside the circle or outside the circle. Justify your answers. a.) (2, 7) Step 1: Use the distance formula to find the length from the center to the given point. D = 13 This point is outside of the circle because the distance is greater than the radius.

11. Example 4 - Continued The center has a center of (-3, -5) and a radius of 6. Determine whether the given point is on the circle, inside the circle or outside the circle. Justify your answers. b.) (-1, 0) Step 1: Use the distance formula to find the length from the center to the given point. D ≈ 5.385 This point is inside of the circle because the distance is less than the radius.

12. Example 5 The endpoints of a diameter of a circle are (7, 12) and (-5, -6). Find the center of the circle. Step 1: Use the midpoint formula to find the center of the circle.