Unit 1
The definition of Geometry
What is the measuring of the earth?
The definition of a line segment
What is a straight path with two distinct endpoints and a fixed length?
The three types of transformations.
What is translation, reflection, and rotation?
The total amount of degrees in a triangle.
What is 180°?
The total amount of degrees in a quadrilateral.
What is 360°?
State the next three terms in the pattern.
0,105,210,315
What is 420,525,630?
Explanation: The pattern is to add 105 to the previous number in the sequence making the new number.
The measure of angle XYZ is 164 degrees. If ray YQ bisects angle XYZ, then what is the measure of angle XYQ.
What is 82°?
Explanation: If YQ bisects XYZ it means XYZ is split right down the middle, making two identical angles. Since 164 divided 2 is 82, XYQ is 82°.
Which way do rotations happen.
What is counter-clockwise?
Determine whether or not the three given lengths could form a triangle.
18 inches, 7 inches, 13inches
Explanation: As long as a triangle's short and medium sides added up are greater than the long side, the triangle is possible.
The difference between a concave and convex polygon.
What is a concave polygon has a point that goes inwards, while a convex polygon only has points shotting outwards.
Determine if the following statement could be written as a biconditional statement. If so, write the statement as a biconditional. If not, explain why not.
If someone lives in the Northern hemisphere, then they live above the equator.
What is true?
Explanation: North is above south, therefore the Northern hemisphere is above the south. Meaning it is also above the Southern hemisphere as well.
What is wrong with the following statement?
Point A ≅ Point B
What is points don't have length and therefore can't be congruent?
What is the equation for rotating 270° ccw.
What is (x,y) → (y,-x)?
Triangle SAM ≅ triangle HQT so that MS ≅ TH, angle M ≅ angle T, and MA ≅ TQ. Determine which one of the congruence conjectures applies to the triangle.
What is SAS?
Explanation:SAS Therom
A quadrilateral with four congruent sides.
What is rhombus?
Decide if the statement is true or false. Then prove or disprove the statement.
A rectangle that is cut in half will create two equal squares.
What is false?
Explanation: The rectangle can be cut in half horizontally, making two smaller rectangles.
The equation of line AB is y=1/2x-1 and point A is located at (4,1)
Write the equation of a line that passes through point A and is perpendicular to line AB.
What is y=-2x-1?
Explanation: To make a perpendicular line the equation must be the reciprocal
Give the coordinates to transform line segment GH using the rule (x,y) → (x+1, y+4) where G is (3,-3) and H is (-3,-2)
What is G=(4,1) and H=(-2,2)
Mrs. Lorentz asks each student in the class to construct a triangle ABC where AB=3 inches, BC=4 inches, and AC=5 inches. How many different triangles are possible that meet these criteria?
A) None
B) Exactly one
C) Two
D) Infinitely many
What is "B"?
Quadrilateral FLAG has coordinates given by F(10,7), A(10,2), and G (8,6). Find the coordinates of point L so that FLAG is a rectangle.
What is L=(10,4.5)
Explanation: First find the two points in between point L, which is "F" and "A". Then use the midpoint formula to find where point L is.
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. Decide if the following statement would prove or disprove his conjecture.
Collin rolled a "2" on five of the nine rolls.
What is prove?
Explanation: this action shows Collin rolled an even number majority of his nine rolls.
Fill in the blank to make the statement true.
The lines with equations 2x+4y=8 and y=___x+10 are parallel.
What is -1/2?
Explanation: First leave the 4y variable by subtracting 2x and putting it's reciprocal -2x on the other side of the equal sign. Next isolate the "y" by dividing by 4 on each side. Leaving the equation -2/4 and 8/4, since the two can be divided by 2 the -2/4 turns into 1/2
Polygon FGHI and polygon LMNO are congruent such that FGHI ≅ LMNO. The following measures are known: GH= 5.6cm, angle L=42°, OL=2.1cm
What other side(s) and angle(s) measures can be found? Identify the sides and angles and give their measures.
What is angle F=42°, IF=2.1cm, MN=5.6cm?
Classify triangle EGH where E=(-7,5), G=(-3,8), and H=(4,4) as either scalene, isosceles, or equilateral. Justify your answer.
What is scalene?
Explanation: Using the distance formula you can find the length of each side.
Three vertices of quadrilateral FISH are given by F (8,3), I (11,-1), and S (10,-4). Find the coordinates of H so that FISH is a parallelogram.
What is H=(7,0)?