Foundations
Name the three undefined terms in geometry
Point, line, and plane.
Name the transformation that slides a figure without turning, flipping, or resizing it.
Translation
If segment AB is congruent to segment CD and AB = 12, what is CD?
12
What is the measure of a straight angle?
180 degrees.
What does it mean to bisect a segment?
Divide it into two congruent segments.
Two lines lie in the same plane and never intersect. What type of lines are they?
Parallel lines.
A figure is turned 90 degrees counterclockwise about point N. Name the transformation and its center.
Rotation; center N.
If M is the midpoint of segment AB and AM = 9, find AB.
18
If a ray divides an angle into two adjacent angles measuring 35 degrees and 48 degrees, find the whole angle.
83 degrees.
What does it mean to bisect an angle?
Divide it into two congruent angles.
Two lines do not intersect and do not lie in the same plane. What type of lines are they?
Skew lines.
A figure is flipped across a line. What is the transformation, and what is the special line called?
Reflection; the line of reflection.
Segment TW is congruent to segment MH. TW = 5y + 10 and MH = 9y - 46. Find y.
y = 14
If a ray bisects a 76 degree angle, what is the measure of each smaller angle?
38 degrees.
What two conditions make a line a perpendicular bisector of a segment?
It passes through the segment's midpoint and is perpendicular to the segment.
What must be true when two lines are perpendicular?
They intersect to form right angles (90 degrees).
A triangle and its image have the same angle measures and side lengths. Name a type of transformation that could produce this and the general class it belongs to.
A translation, rotation, or reflection; it is a rigid motion/isometry.
TM bisects segment HW at T. HT = 5k + 12 and TW = 10k - 23. Find k.
k = 7
Angles RKH, HKD, and DKT are adjacent. Their measures are 4y, 6y - 16, and 2y + 4, and together they form 132 degrees. Find y.
y = 12
KM is a perpendicular bisector of segment RY at midpoint W. What relationship must be true between RW and WY?
RW = WY.
Explain the difference between parallel lines and skew lines.
Parallel lines are coplanar and never intersect; skew lines are noncoplanar and never intersect.
DAILY DOUBLE: A figure is enlarged from a center point so that every image length is twice the corresponding preimage length. Name the transformation and scale factor.
Dilation with scale factor 2.
Using the previous situation, HT = TW when k = 7. Find the full length HW.
94
DAILY DOUBLE: Using y = 12 in the previous clue, find the measure of angle HKT (angles HKD + DKT).
*Angles RKH, HKD, and DKT are adjacent. Their measures are 4y, 6y - 16, and 2y + 4, and together they form 132 degrees. Find y.
132? Correction: HKD = 56 degrees and DKT = 28 degrees, so HKT = 84 degrees.
If a point lies on the perpendicular bisector of a segment, how are its distances from the two endpoints related?
The point is equidistant from the two endpoints.