Distance
What is −7+12?
5
The sequence is: 4, 7, 10, 13, …
What is the next number?
16
True or False:
“If two angles are both 90°, then they are congruent.”
True
If ∠A = 25°, find its complement.
65°
Sara is standing at point –7 on a number line. Her friend is at point 3. How far apart are they?
10 units
What does bisectors mean?
A line segment bisector cuts a line segment into two equal pieces.
An angle bisector splits an angle into two equal angles.
3² = 9
5² = 25
7² = 49
What conjecture can you make?
The square of an odd number is always odd.
Given: All squares have four right angles.
Shape A is a square.
What can you conclude?
Shape A has four right angles.
If ∠B = 110°, find its supplement.
70°
Point M is at –18 and point N is at 7.
What is the distance between M and N?
25 units
The points A and B are at 4 and 10 on a number line. What is the midpoint of segment AB?
7
1, 2, 4, 8, …
What is the pattern and the next term?
×2 each time; next term = 16.
You see three triangles with angle sums of 180°.
You guess all triangles have angle sums of 180°.
Is that inductive or deductive?
Inductive
∠C and ∠D form a linear pair. If ∠C = 72°, find ∠D.
108°
A robot is at position –25 on a number line, and a drone is at position 40. What is the distance between them?
65 units
Find the midpoint of the segment with endpoints (2,3) and (6,7)?
(4,5)
1² + 2² = 5
4² + 5² = 41
6² + 7² = 85
What conjecture can you make?
The sum of two consecutive squares is always odd.
Given: If two angles add to 180°, they are supplementary.
Angles X and Y are supplementary.
Conclusion: X + Y = 180°.
Valid
In a diagram, ∠X and ∠Y share a straight line. What type of angle pair are they?
Linear pair (so supplementary)
Point R is at –42 and point S is at 19.
What is the distance between R and S?
61 units
T is the midpoint of segment RS. If RT = 2x+32x + 32x+3 and TS = x+5x + 5x+5, what is x?
2
Conjecture: “All polygons have equal sides.”
Give a counterexample.
A rectangle (not all sides are equal).
If it rains, the field gets wet.
If the field gets wet, practice is canceled.
What conclusion can you make?
If it rains, practice is canceled.
If two lines look perpendicular but there is no right-angle symbol, can you assume they are perpendicular?
No