Unit 1
What is a conditional statement?
A statement that relies on the idea of if p, then q. (If one something happens, then something else happens).
What is the definition of bisecting?
Bisecting is to divide an angle, line, or shape in half.
What is translation?
A geometric transformation that moves a line, point, or shape in the same direction.
What theorem is it when a line is congruent to itself?
Reflexive Property of Equality.
What is the definition of a quadrilateral with four equal sides and perpendicular diagonals with four right angles?
Square. Both rhombuses and squares have four equal sides with diagonals that are perpendicular, but a rhombus does not have four right angles, while a square does. Therefore, the quadrilateral is a square.
Identify the condition and the conclusion of the statement.
"If it flies, it must be a bird."
Condition: "If it flies,"
Conclusion: "Then it must be a bird."
Rewrite the statements in geometric notation.
a. Line OP bisecting line segment AZ
b. Line AB parallel to line CD
a. OP _|_ AZ
b. AB || CD
Translate right 4 units.
What is the definition of a scalene triangle?
A triangle with three side and angle lengths of different values.
Complete the sentence with sometimes, always, or never.
A rhombus is ______ a square.
Sometimes. All squares are considered rhombuses, but rhombuses cannot be considered squares as they do not have four right angles. Therefore, rhombuses are not always squares.
Rewrite the following statement in if, then form.
Pasta served with tomato sauce is spaghetti.
Angle A and B are vertical angles.
Angle A=4x+8
Angle B=7x-10
Find the value of x.
4x+8=7x-10
-4x -4x
8=3x-10
+10 +10
18=3x
6=x
y=|x| is translated 9 units left and 5 units down. Write the equation for the transformation.
y=|x+9|-5
In triangles LAG and BED, line LA=BE and line AG=ED. What other statement is need to prove LAG=BED by the SAS Congruence Conjecture?
Angle A=Angle E.
(n-2)180.
(20-2)180.
(18)180.
3240.
Jonathan analyzes birds in the park every day of the week. He notices that ducks appear on Thursdays, but not on Mondays and bluebirds appear weekends but not weekdays. What is a logical conclusion that can be drawn from this statement?
A) The ducks migrate away from the park on Mondays.
B) Geese appear in the park on Mondays.
C) The ducks only appear on Thursdays.
D) The bluebirds will not appear on Fridays.
Point F is located at (6,15). Point S is located at (10,21). Find the midpoint of line segment FS.
(xm,ym)=(x1+x2)/2, (y1+y2)/2
(6+10)/2, (21+15)/2
16/2, 36/2
(8, 18)
Point B (5,6) is transformed with rule (x,y)>(x+4,y+5). Find the coordinates of Point B'.
(5,6)
(x+4,y+5)
(5+4,6+5)
Point B'=(9,11)
AVX is an isosceles triangle. AV=24. AX=x2+5x. Find the values of x.
x2+5x-24=0
(x+8)(x-3)
x=-8 and x=3
Square FISH has a side length of 8. Why must the perimeter of FISH be 32?
In a square, all four side lengths are congruent. There are four side lengths with lengths of eight, and 4x8=32. Therefore, the perimeter must be 32.
The first six shapes in a pattern are:
+-==-+
What will the 100th shape be?
The equal will be the 100th shape in the sequence. If we continue the 6 shape pattern, it will go to 96 as 6x16=96. The next 4 shapes will be +-==, with =being the 100th shape. Therefore, the = is the 100th shape.
Line YZ is equal to y=1/2x-2. Write a line that is perpendicular to line YZ.
Answers will vary, but should include y=-2x. Perpendicular lines have slopes that are opposite reciprocals, and the opposite reciprocal of 1/2 is -2.
Point Y (5,9) will be reflected over the x-axis and then rotated 90 degrees counterclockwise about the origin. Give the coordinates of Y' and Y''.
E= (5,9)
Reflection over x-axis: (x,y) --> (x,-y)
E'= (5,-9)
Rotation 90 degrees clockwise: (x,y) --> (-y,x)
E''= (-9,5)
Determine if the two triangles are congruent.
These triangles are not congruent. In both, there are three angles that are revealed. There is no AAA Congruence theorem, so these two triangles cannot be congruent, as the side lengths can be of varying lengths.
Quadrilateral ROCK has vertices R(2,7), O(2,-2), C(6,-2), and K(6,7). What is the most specific name of the quadrilateral?
Rectangle. Line RO is parallel to line KC, and line RK is parallel to line OC. The lines are also perpendicular with the slopes being opposite reciprocals (0 and unidentified). The side lengths are also not the same, so the shape is a rectangle and not a square.