Unit 1
What is a bi-conditional statement?
a two-way statement that combines a conditional statement and its converse, meaning both "if P then Q" and "if Q then P" are true.
What does perpendicular mean?
Describes lines, rays, or segments that intersect to form a perfect right angle, which measures exactly 90 degrees (90°), often shown with a small square symbol at the corner.
The point Q(-10,4) is transformed according to the translation rule (x, y) --> (x+14, y-8). Give the coordinates of Q'
Q' (4,-4)
RS and ST are congruent, If RT equal 12 and RS equal 10 what is ST.
10
True or False Parallel has two sets of parralel lines.
True
Identify the classification and the differenciation of the statement.
A vehicle with two wheels in tandem, usually propelled by pedals connected to the rear wheel by a chain, and having handlebars for steering and a saddlelike seat.
LM=MN
LN=18
Find the length of LM
LM=9
Triangle JKL has coordinates given by J (3,8), K(-2,5) and L(-4,-1). After a translation coordinates of L' are (1,-3) Find J' and K'
(x,y) --> *(x+5 y-2)
J'= (8,6)
K'=(3,3)
In triangle OPA, the measure of angle A is 5 degrees less than the measure of angle P. The measures of angle O is 20 degrees less than the measure of angle A. Find the measures of the three angles.
O=45 A=65 P=70
A rectangle is sometimes, always, or never a square.
Sometimes
Is the statement, "If it is Christmas Day, then the date of the calendar is December 25th a biconditional, if so what is the biconditional statemet.
Yes; If the date on the calendar is December 25, then it is Christmas Day.
The length of EG is 30 inches.
The length of FG is 12 inches.
What is the length of EF
18
Point L (21,15) is translated such that the image is L' (35, -10). Write a rule for the translation.
(x,y) --> (x-14,y+25)
A ladybug starts at the origin of a coordinate plane, then crawls 4 units to the right and 7 units down. What are the coordinates of the point where the ladybug lands?
(4, -7)
A trapezoid is always, sometimes, or never an isosceles trapezoid.
Sometimes
Collin rolled a 6- sided die several times. He made a conjecture that he would roll more even numbers than odd numbers during his next 9 rolls. Does the statement "Collin rolled a "2" on five of the nine rolls prove, disprove, or neither prove nor disprove his conjecture.
Prove because that means he got equal on most of its rolls.
Point P is the midpoint of line segment MN. Point M is located at (-12, -5) and point P is located at (2,-3). What are the coordinates of point N.
N=(16,-1)
Point L (21,15) is reflected such that the image is L' (21,-15).
Describe the transformation in words then write a rule for the transformation.
The transformation is reflected over the x-axis.
(x,y) --> (x-y)
Determine whether triangle ABC with vertices A (2,4) B(10,4) and C(7,7) is right, acute, or obtuse. Justify your answer.
AB=8 and C=obtuse a squared+ b squared+ c squared=obtuse.
A trapezoid is always sometimes or never a quadrilateral.
Always
300 students are in the cafeteria. Today is school spirit day and students receive one point for wearing something red and one point for wearing something blue. 135 students earned the "red" point and 175 students earned the "blue point". If 15 students did not earn any points then how many students earned both the "red" and the "blue" points?
25 students.
The equation of MN is y=2/3x-10 and point P is located at (0,-10). Write the equation of a line that passes through point P and is neither parallel or perpendicular to line MN.
y=x-10
Line segment LG has end points L(7,12) and G(5,8). Find the coordinates of L' and L'' after the line segment is translated 4 units left and then reflected over the y-axis.
L' (3,12) G' (1,8)
L''(-3,12) G''(-1,8)
Polygon FGHI and polygon LMNO are congruent such that FGHI is congruent to LMNO. The following measures are known:
GH=5.6 cm
m<L=42 degrees
OL=2.1 cm
What other side(s) and angle(s) measures can be found? Identify the sides and angles and give their measures.
MN=5.6
m<F=42 degrees
IF=2.1 cm
A quadrilateral is always sometimes, or never a parallelogram.
sometimes.