Logic & Conjectures
What is a Conjecture
Educated guess
What is a conditional statement
An If-then statement
If AB = BC and BC = CD, what property proves AB = CD?
Transitive Property of Equality
Draw a transversal and name all the corresponding angles, and all the alternate interior angles
Your choice
What must be true on order for the lines to be parallel/perpendicular
Parallel: Same slope
Perpendicular: Opposite reciprocal slopes.
What is a Counterexample?
One example that contradicts the conjecture.
What is the converse of: If two angles are vertical angles, then they are congruent?
Is that True?
If two angles are congruent, then they are vertical angles. Must provide counter Example
If ∠1 and ∠2 form a linear pair and m∠1 = 118°, find m∠2 and state the Theorem
62, Supplement Theorem/Linear Pair Theorem
What is the difference between a parallel line and a skew lines.
Parallel line are coplanar lines that do not intersect and skew lines are non coplanar line that do not intersect
Write slope intercept form, point slope form, Horizontal line equation, Vertical line equations.
y=mx+b
y-y1=m(x-x1)
y=a
x=a
If the quadrilaterals have the same area, then they are congruent.
rectangle with sides 2 and 8 (Area = 16) and a square with side 4 (Area = 16).
What is the inverse of: If a figure is a square, then it has four sides?
If a figure is not a square, then it does not have four sides
Given: ∠ A and ∠ C are complementary
∠B and ∠C are complementary
Prove: ∠ A ≅ ∠ B
Multiple answers
Alternate interior angles are congruent to each other as long as the lines intersecting the transversal are not congruent. True or false
False
Is this Perpendicular, Parallel or neither:
y = 3x + 2 and y = -1/3x + 5
Perpendicular
Make a conjecture: 1,2,6,24,120,.....
each term is multiplied by an increasing number. the next term would be 96*5=480.
If p is false and q is false, is 'If p, then q' true or false?
True
What does the congruent Supplement theorem state. Draw or Write it.
If ∠ 1 and ∠ 2 are supplementary and ∠ 2 and ∠ 3 are supplementary then ∠ 1 and ∠ 3 are congruent.
What does the Perpendicular Transversal theorem state?
IF a line is perpendicular to one of the two parallel lines, then it is perpendicular to the to other.
Write an equation in slope intercept form for the line perpendicular to y=1/3x-5 that contains (3,5)
y=-3x+14
If 2 angles are same side interior then they are congruennt
False, Must provide counter example
Write the conditional, converse, and if there is a biconditional. If two angles form a linear pair, then they are supplementary.
• Conditional Statement (p->q): If two angles form a linear pair, then they are supplementary. (True)
• Converse Statement (q->p): If two angles are supplementary, then they form a linear pair. (False).
No biconditional
Given: ∠ 1 ≅ ∠ 3
Prove: ∠ 2 ≅ ∠ 4
Without using Corresponding angle Converse Thereom
Multiple answers
Find x, y, and ∠1, ∠2
Mr. O'Donnell draw pic
x=90
y=26.66
1=130
2=50
Line L passes through A(-4,7) and B(2,-5).
Line M passes through C(3,k) and D(7,1).
1. Find the slope of line L.
2. If line M is perpendicular to line L, find the value of K
3. A student claims that line m is parallel to a line with slope -2. Explain why the student is correct or incorrect.
1. -2
2. k=-1
3. The student is incorrect. Parallel lines must have the same slope. Line M has slope 1/2, not -2.