Transcript 1 2 Segment Congruence

1.2: Use Segments & Congruence
Objectives:
1. To use the Ruler
and Segment
Addition Postulates
2. To construct
congruent segments
with compass and
straightedge
Assignment:
• P. 12-14: 1, 3-12 M3,
17, 20, 22, 29, 30, 37,
38
• Challenge Problems
You will be able to construct congruent
segments with compass and straightedge
Congruent Segments
Congruent segments are line segments
that have the same length.
Numbers:
𝐴𝐶 = 𝐷𝐶
Shapes:
𝐴𝐶 ≅ 𝐷𝐶
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!
Copying a Segment
1. Draw segment AB.
Copying a Segment
2. Draw a line with point A’ on one end.
Copying a Segment
3. Put point of compass on A and the pencil
on B. Make a small arc.
Copying a Segment
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’.
Objective 2
You will be able to use
the Ruler and Segment
Addition Postulates
Exercise 1
What is the length of 𝐴𝐵?
B
A
Exercise 1
You basically used the Ruler Postulate to
find the length of the segment, where A
corresponds to 0 and B corresponds to 6.5.
So AB = |6.5 – 0| = 6.5 cm
B
A
Exercise 2
Now what is the length of 𝐴𝐵?
B
A
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.
Exercise 3
When asked to measure the segment below,
Kenny gave the answer 2.7 inches.
Explain what is wrong with Kenny’s
measurement.
Give Them an Inch…
A Standard English ruler has 12 inches.
Each inch is divided into parts.
•
•
•
•
Cut an inch in half, and you’ve got 1/2 an inch.
Cut that in half, and you’ve got 1/4 an inch.
Cut that in half, and you’ve got 1/8 inch.
Cut that in half, and you’ve got 1/16 inch.
Click me!
Exercise 4
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).
Exercise 5
Use the diagram to find 𝐺𝐻.
Exercise 5
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?
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.
Exercise 6
Point 𝐴 is between 𝑆 and 𝑀. Find 𝑥 if 𝑆𝐴 =
2𝑥 − 5, 𝐴𝑀 = 7𝑥 + 3, and 𝑆𝑀 = 25.
Exercise 7
Point 𝐸 is between 𝐽 and 𝑅. Find 𝐽𝐸 given
that 𝐽𝐸 = 𝑥 2 , 𝐸𝑅 = 2𝑥, and 𝐽𝑅 = 8.
Exercise 8: SAT
Points 𝐸, 𝐹, and 𝐺 all lie on line 𝑚, with 𝐸 to
the left of 𝐹. 𝐸𝐹 = 10, 𝐹𝐺 = 8, and 𝐸𝐺 >
𝐹𝐺. What is 𝐸𝐺?
1.2: Use Segments & Congruence
Objectives:
1. To use the Ruler
and Segment
Addition Postulates
2. To construct
congruent segments
with compass and
straightedge
Assignment:
• P. 12-14: 1, 3-12 M3,
17, 20, 22, 29, 30, 37,
38
• Challenge Problems