Vocabulary
Explain what a "conditional statement" is in your own words.
A conditional statement is an "if-then" statement where the first part (the hypothesis) leads to the second part (the conclusion).
What is the distance formula used to find the distance between two points (x1,y1) and (x2,y2)?
d=sqrt(x2−x1)2+(y2−y1)2
Find the midpoint of the segment connecting points (1, 2) and (3, 4)
(2,3)
What is a conditional statement? Provide an example.
A conditional statement is a logical statement that has the form "If P, then Q." Example: "If it rains, then the ground is wet."
Define "colinear"
Points lie on the SAME line
Define the term "inverse" in relation to conditional statements.
The inverse of a conditional statement is formed by negating both the hypothesis and conclusion. For example, the inverse of "If P, then Q" is "If not P, then not Q.
If point A is at (2, 3) and point B is at (5, 7), what is the distance between them?
5
What is the midpoint formula for finding the midpoint between two points (x1,y1) and (x2,y2)?
M=(x1+x2/2, y1+y2/2)
Define the converse of a conditional statement
The converse of a conditional statement "If P, then Q" is "If Q, then P." Switch the hypothesis and the conclusion.
What is the difference between parallel and perpendicular lines?
Parallel lines never intersect. Perpendicular lines intersect at a 90 degree angle (right angle).
Define the term "Congruent"
Congruent means that two figures have the same shape and size.
Point A is located at (10,-5) and point B is located at (-2,7). Set up the distance formula for the distance from point A to B.
d= sqrt((-2-10)2+(7-(-5))2)
Triangle ABC has Coordinates A (-3, -5), B (0,-1), and C(3,-3). Find the midpoint of AC.
(0,-4)
What is the contrapositive of the statement "If it rains, then the ground is wet"?
The contrapositive is "If the ground is not wet, then it does not rain."
Supplementary vs Complementary Angle measures?
Supplementary angles add up to 180 degrees. Complementary angles add up to 90 degrees.
What does "counterexample" mean? Give an example.
A counterexample is an example that disproves a statement. For instance, the statement "All birds can fly" can be disproved by the counterexample of an ostrich.
Find the distance between the points (6, -2) and (-4, 5) using the distance formula.
12.21
If a point is halfway between (4, 10) and (8, 14), what are the coordinates of that point?
(6, 12)
Explore the relationship between a conditional statement and its inverse
The inverse of a conditional statement "If P, then Q" is "If not P, then not Q." The truth of a conditional does not imply the truth of its inverse.
What is a conjecture? A postulate? And a theorem?
C: Educated guess. Made based on patterns or observations
P: Accepted as true w/out proof
T: True with proof/evidence
Define the term "Contrapositive".
This is when you negate and switch the hypothesis and the conclusion of a conditional statement.
On a map, Mark’s house is located at ( -6, -2) and Lucy’s house is located at (0, -2). What is the distance between Mark’s house and Lucy’s house?
6
Is the midpoint a length in units or written as a coordinate?
coordinate
Write your own conditional statement. Underline the hypothesis and circle your conclusion.
...
What is the relationship between a statement and its contrapositive?
A statement and its contrapositive are logically equivalent; if one is true, the other is also true.