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Warm Up
Over Chapter 1
Find SR if R is the midpoint
of SU shown in the figure.
A. 22
B. 16
C. 4
D. 0
Chapter 2 Section 1
Take Note
Inductive Reasoning
Description: using a number of specific examples
to arrive at a conclusion
Example: 6, 12, 18, 24, ….
The conclusion you come up
with is called a conjecture
Conjecture: Adding 6 to the previous term
For Example
Patterns and Conjecture
A. Write a conjecture that describes the pattern
2, 4, 12, 48, 240. Then use your conjecture to find
the next item in the sequence.
Step 1
Look for a pattern.
2
4
12
48
240
Step 2
×2
×3
Make a conjecture
×4
×5
The numbers are multiplied by 2, 3, 4, and 5. The next
number will be multiplied by 6. So, it will be 6 ● 240 or
1440.
Answer: 1440
Patterns and Conjecture
For Example
B. Write a conjecture that describes the pattern
shown. Then use your conjecture to find the next
item in the sequence.
Step 1
Look for a pattern.
3
9
+6
18
+9
For Example
Step 2
Patterns and Conjecture
Make a conjecture.
Conjecture: Notice that 6 is 3 × 2 and 9 is 3 × 3. The
next figure will increase by 3 × 4 or 12
segments. So, the next figure will have
18 + 12 or 30 segments.
Answer: 30 segments
Check
Draw the next
figure to check
your conjecture.
You Try
A. Write a conjecture that describes the pattern in
the sequence. Then use your conjecture to find the
next item in the sequence.
A.
B.
C.
D.
You Try
B. Write a conjecture that describes the pattern in
the sequence. Then use your conjecture to find the
next item in the sequence.
1
3
6
10
For Example
A. Make a conjecture about the product of two odd
numbers.
Take Note
Counterexample
Description: a false example. It shows a
conjecture cannot be true.
Example: If ∠A and ∠B are complementary, then
they share a common side.
Counterexample:
You Try
Find Counterexamples
Find a counterexample to show this conjecture is false:
A. If a ray intersects a segment at its midpoint, then
the ray is perpendicular to the segment.
Perpendicular = intersects at a right angle 
Homework
• HW 10: Pg.94 #’s 1-8, 12-16, 31, 40, 42