1 2 Measuring and Constructing Segments 1 1

1 -2 Measuring and Constructing Segments 1. 1 Exit Ticket: Part 1 Answers 1. Two opposite rays. CB and CD 2. A point on BC. Possible answer: B, C, D 3. The intersection of plane N and plane T. Possible answer: BD 4. A plane containing E, D, and B. Plane T Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Exit Ticket: Part II Answers Draw each of the following. 5. a line intersecting a plane at one point 6. a ray with endpoint P that passes through Q Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Objectives 1. Use Segment Addition Postulate and Midpoint 2. Construct Congruent segment and Midpoint AB Length of AB (distance between A & B) AB line segment AB AB line AB Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Find the distance between two points or the length of the segment Example. Find the length of EF, FC, DC Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Find the distance between two points or the length of the segment You Practice. Find the length of DB and DC Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Congruent segments: segments that have the same length. In the diagram, PQ = RS, so you can write: PQ RS. This is read as: “segment PQ is congruent to segment RS. ” Tick marks are used in a figure to show congruent segments. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments In order for you to say that a point B is between two points A and C, all three points must lie on the same line, and AB + BC = AC. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 1 A: Using the Segment Addition Postulate G is between F and H, FG = 6, and FH = 11. Find GH. 1. Draw picture 2. Write equation based on picture. 3. Solve Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 1 B: Using the Segment Addition Postulate R is between T and M, RT = 7, and RM = 12. Find TM. 1. Draw picture 2. Write equation based on picture. 3. Solve Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Check It Out! Example 1 Y is between X and Z, XZ = 15, and XY =2 Find YZ. XZ = XY + YZ Holt Mc. Dougal Geometry .

1 -2 Measuring and Constructing Segments Challenge: Using the Segment Addition Postulate M is between N and O. Find NO. Seg. Add. Postulate Substitute the given values Simplify. Subtract 2 from both sides. Subtract 3 x from both sides. Divide both sides by 2. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Challenge: Using the Segment Addition Postulate E is between D and F. Find DF. Seg. Add. Postulate Substitute the given values Simplify. Subtract 3 x from both sides. Divide both sides by 3. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Midpoint: Bisect: Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments The midpoint M of AB is the point that bisects, or divides, the segment into two congruent segments. If M is the midpoint of AB, then AM = MB. So if AB = 6, then AM = 3 and MB = 3. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Construct Midpoint and segment bisector Math Open Reference http: //www. mathopenref. com/tocs/constructionst oc. html Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 2 A: Using the Midpoint S is the midpoint of JK, and SJ = 4. Find JK 1. Draw picture 2. Write equation based on picture. 3. Solve Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 2 B: Using the Midpoint B is the midpoint of AC, and AB = 22. Find BC 1. Draw picture 2. Write equation based on picture. 3. Solve Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 3: Using Midpoints to Find Lengths D is the midpoint of EF, ED = 4 x + 6, and DF = 7 x – 9. Find ED, DF, and EF. E 4 x + 6 D 7 x – 9 F Step 1 Solve for x. D is the mdpt. of EF. Substitute 4 x + 6 for ED and 7 x – 9 for DF. Subtract 4 x from both sides. Simplify. Add 9 to both sides. Simplify. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Example 3: Using Midpoints to Find Lengths D is the midpoint of EF, ED = 4 x + 6, and DF = 7 x – 9. Find ED, DF, and EF. E 4 x + 6 D 7 x – 9 F Step 1 Solve for x. D is the mdpt. of EF. Substitute 4 x + 6 for ED and 7 x – 9 for DF. Subtract 4 x from both sides. Simplify. Add 9 to both sides. Simplify. Holt Mc. Dougal Geometry

1 -2 Measuring and Constructing Segments Check It Out! Example 3 S is the midpoint of RT, RS = – 2 x, and ST = – 3 x – 2. Find RS, ST, and RT. R – 2 x S – 3 x – 2 T Step 1 Solve for x. S is the mdpt. of RT. RS = ST – 2 x = – 3 x – 2 Substitute – 2 x for RS and – 3 x – 2 for ST. +3 x Add 3 x to both sides. x = – 2 Holt Mc. Dougal Geometry Simplify.

1 -2 Measuring and Constructing Segments HW • Pg 17, 1 -7, 18 Holt Mc. Dougal Geometry