1. Objective: Determine if triangles in a coordinate plane are similar. What do we know about similar figures? (1)Angles are congruent (2)Sides are proportional What are the three theorems we use to prove triangles similar? AA~, SAS~, and SSS~ 1 6.2.1: Midpoints and Other Points on Line Segments

2. Key Concepts A line segment in a coordinate plane is noted by two endpoints, (x 1, y 1 ) and (x 2, y 2 ). The length of a line segment can be found using the distance formula,. The midpoint of a line segment is the point on the segment that divides it into two equal parts. 2 6.2.1: Midpoints and Other Points on Line Segments

3. Key Concepts, continued Finding the midpoint of a line segment is like finding the average of the two endpoints. The midpoint formula is used to find the midpoint of a line segment. The formula is. You can prove that the midpoint is halfway between the endpoints by calculating the distance from each endpoint to the midpoint. It is often helpful to plot the segment on a coordinate plane. 3 6.2.1: Midpoints and Other Points on Line Segments

4. Guided Practice Example 1 Calculate the distance of the line segment with endpoints (–2, 1) and (4, 10). 4 6.2.1: Midpoints and Other Points on Line Segments

5. Guided Practice Example 2 Calculate the midpoint of the line segment with endpoints (–2, 1) and (4, 10). 5 6.2.1: Midpoints and Other Points on Line Segments

6. Guided Practice: Example 1, continued 6 ✔ The midpoint of the segment with endpoints (–2, 1) and (4, 10) is (1, 5.5). 6.2.1: Midpoints and Other Points on Line Segments

7. Guided Practice Example 2 Show mathematically that (2, 1) is the midpoint of the line segment with endpoints (-1, -2) and (5, 4) by finding the distance between the endpoints and the midpoint. 7 6.2.1: Midpoints and Other Points on Line Segments

8. Ticket-Out the Door 8 Are these two triangles congruent AB= BC= AC= RP= QP= RQ=