Chapter 1 1-2 measuring and constructing segments Geometry Chapter 1 1-2 measuring and constructing segments

Warm up 1. Name three collinear points 2. Name two opposite rays 3. A plane containing E, D, and B. Draw each of the following 4. a line intersecting a plane at one point 5. a ray with endpoint P that passes through Q

Warm up answers 1. Name three collinear points Answer: B,C and D 2. Name two opposite rays Answer: CB and CD 3. A plane containing E, D, and B. Plane T Draw each of the following 4. a line intersecting a plane at one point 5. a ray with endpoint P that passes through Q

Objectives Students will be able to: Use length and midpoint of a segment. Construct midpoints and congruent segments.

Measuring and constructing segments A ruler can be used to measure the distance between two points. A point corresponds to one and only one number on a ruler. The number is called a coordinate. The following postulate summarizes this concept.

Measuring and constructing segments The distance between any two points is the absolute value of the difference of the coordinates. If the coordinates of points A and B are a and b, then the distance between A and B is |a – b| or |b – a|. The distance between A and B is also called the length of AB, or AB. AB = |a – b| or |b - a| A a B b

Example 1 Find each length AB AC AB=|-2-1| AC=|-2-3| =|-3|=3 =|-5|=5

Example 2 Check it out Ex. 1 page 13 Find each length.

Congruent segments are segments that have the same length Congruent segments are 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.

Construction You can make a sketch or measure and draw a segment. These may not be exact. A construction is a way of creating a figure that is more precise. One way to make a geometric construction is to use a compass and straightedge.

Sketch, draw, and construct a segment congruent to MN. Step 1 Estimate and sketch. Estimate the length of MN and sketch PQ approximately the same length. P Q Measure and draw. Use a ruler to measure MN. MN appears to be 3.5 in. Use a ruler to draw XY to have length 3.5 in. Step 3 Construct and compare. Use a compass and straightedge to construct ST congruent to MN.

Segment addition Postulate 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.

Example 3 If B is between A and C and AB is 7 and AC is 20. Find the length of BC. Answer: AC=AB+BC segment addition postulate 20=7+BC substitute the values of AC and AB -7 -7 then solve for BC 13= BC

Example 4 Let’s say S is in between R and T and RS= x+4 and ST=2x+6. Find RT. Solution: RT=RS+ST using segment addition postulate 𝑅𝑇= 𝑥+4 + 2𝑥+6 𝑅𝑇= 𝑥+2𝑥 + 4+6 add common terms and simplify 𝑅𝑇=3𝑥+10

Example 5 Let B be in between A and C. If AB =4x-5 and BC= 5x+7. If AC= 47. Find x. Solution: AC=AB+BC using adding segment postulate 47= 4𝑥−5 + 5𝑥+7 substitute AB,BC and AC 47= 4𝑥+5𝑥 + −5+7 combine like terms and simplify 47=9𝑥+2 simplify and solve for x -2 -2 45=9𝑥 solve for x 45 9 = 9𝑥 9 𝑥=5

Midpoint of a segment What is a Midpoint of a segment? Solution: 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. A segment bisector is any ray , segment or line that intersects the segment at its midpoint. It divides the segment into two equal parts just like the midpoint.

Example 6 D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. Solution: ED = DF D is the mdpt. of EF. 4x + 6 = 7x – 9 Substitute 4x + 6 for ED and 7x – 9 forDF Subtract 4x from both sides. 6 = 3x – 9 Simplify. +9 +9 15 3 =3𝑥 solve for x 5=x or x=5 –4x –4x

Homework Chapter 1-2 homework Do the Worksheet

Closure Today we learned about constructing segments, segment addition postulate and the midpoint Tomorrow we are going to continue with section 3.