Name: ______Date: ______
DO NOW: Make an isometric drawing.
1.3 Measuring Segments
Objectives: I will be able find and compare lengths of segments and to construct congruent segments with compass and straightedge
Congruent Segments / •Congruent segments are line segments that have the same length. /Copying a Segment / We’re going to try making two congruent segments using only a compass and a straightedge. Here, we’re not using a ruler to measure the length of the segment!
- Draw segment AB.
3. Put point of compass on A and the pencil on B. Make a small arc.
4. Put point of compass on A’ and use the compass setting from Step 3 to make an arc that intersects the line. This is B’. /
Distance / between two points A and B is the absolute value of the difference of their coordinates, or |a - b|.
· The distance is also the length of line segment AB. /
Postulate 1-5: Ruler Postulate / The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is its coordinate.
The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B. /
Let’s say you found the length of a segment to be 6’ 7” using your dad’s tape measure. Convert this measurement to the nearest tenth of a centimeter (1” ≈ 2.54 cm).
Example 1: Measuring Segment Lengths /
Use the diagram to find GH.
Could you as easily find GH if G was not collinear with F and H? Why or why not?
Postulate 1-6: Segment Addition Postulate / •If B is between A and C, then AB + BC = AC.
•If AB + BC = AC, then B is between A and C. /
Example 2: / Point A is between S and M. Find x if SA = 2x – 5, AM = 7x + 3, and SM = 25.
Now You Try: / 1. Point E is between J and R. Find JE given that JE = x2, ER = 2x, and JR = 8.
2. M is between L and N. Find each measurement if: LM = 4x+6 , LN = 5x+10, MN = 3x – 4 /
Example 3: Use the number line below. Tell whether the segments are congruent. /
Midpoint / Is a point that divides the segment into two congruent segments. /
Segment Bisector / A point, line, ray, or other segment that intersects a segment at its midpoint and bisects the segment
Example 4: /
Now You Try: / Q is the midpoint of TV. What are TU, UV, and TV?
1.4 Measuring Angles
OBJECTIVES: I will be able to name, measure and classify angles.
Angle / An angle consists of two different rays (sides) that share a common endpoint (vertex).•Angle ABC, ABC, or B / /
A “Rabbit Ear” antenna is a physical model of an angle
Example 1: / How many angles can be seen in the diagram?
Name all the angles. /
Measure of an Angle / The measure of an angle is the smallest amount of rotation about the vertex from one side to the other, measured in degrees.
•Can be any value between 0 and 180
•Measured with a protractor /
Classifying Angles / Surely you are familiar with all of my angular friends by now.
Example 2: / Write the measure of each angle. Then classify each angle.
Now You Try: / Find the measure of each angle. Then classify each angle as acute, right, obtuse, or straight.
6.
7. /
Example 3 / What is the measure of DOZ? /
Angle Addition Postulate / •If P is in the interior of RST, then
mRST = mRSP + mPST. /
Example 4 / Given that mLKN = 145°, find mLKM and mMKN. /
Congruent Angles / •Two angles are congruent angles if they have the same measure. /
Congruent Angles /
- Draw angle A.
2. Draw a ray with endpoint A’.
3. Put point of compass on A and
draw an arc that intersects both sides of the angle. Label these points B and C.
4. Put point of compass on A’ and use the compass setting from Step 3 to draw a similar arc on the ray.
Label point B’ where the arc intersects
the ray.
- Put point of compass on B and pencil on C. Make a small arc.
- Draw ray A’C’.
Example 5: / In the diagram, YW bisects XYZ, and mXYW = 18°. Find mXYZ. /
Example 6 / In the diagram, OE bisects angle LON. Find the value of x and the measure of each angle. /
SUMMARY:
Assignment: / 1.3 Practice worksheet: # 1 - 20
pg. 31 – 34: # 8 – 14, 22, 23, 29, 30, 33 – 38, 41 - 43