Transformations
What type of transformation slides a figure without rotating or flipping it?
Translation
What does SSS stand for in triangle congruence?
Side-Side-Side
What is the name of a line segment that connects a vertex to the midpoint of the opposite side?
Median
What is the name of the point where the medians of a triangle intersect?
Centroid
What kind of angles are formed when a transversal crosses parallel lines?
Corresponding, alternate interior, alternate exterior, and same-side interior angles
What type of transformation flips a figue over a line?
Reflection
What triangle congruence theorem requires two angles and the included side?
ASA
In a triangle, the largest angle is always opposite the ________.
Longest side
What is the name of the point that is equidistant from all sides of a triangle?
Incenter
True or False: If two lines have the same slope, they are parallel.
True
A rotation of 90° clockwise around the origin maps (3, 4) to what point?
(4,-3)
Why is SSA not a valid triangle congruence theorem in most cases?
It doesn't guarantee congruence (ambiguous case)
The centroid of a triangle divides each median in what ratio?
2:1
What do you call a segment from a vertex perpendicular to the opposite side (or its extension)?
Altitude
What is the slope of a line perpendicular to a line with slope 2?
-1/2
What sequence of transformations maps a figure onto its mirror image across the y-axis and then moves it up 3 units?
Reflection over y-axis, then translation up 3 units
Name all the valid triangle congruence theorems.
SSS, SAS, ASA, AAS, and HL (for right triangles)
A triangle has two sides of lengths 7 and 10. What is the possible range for the third side?
Between 3 and 17 (not inclusive)
What is the name of the point where the perpendicular bisectors of a triangle intersect?
Circumcenter
If two parallel lines are cut by a transversal and one angle is 70°, what is the measure of the alternate interior angle?
70°
A triangle is reflected over the x-axis, then rotated 180° around the origin. Describe the single transformation that is equivalent.
Reflection over the line y = -x
Given △ABC ≅ △DEF, if AB = 5 cm and ∠C = 40°, what are the corresponding parts in △DEF?
DE = 5 cm, ∠F = 40°
Name all four special segments in a triangle and their points of concurrency.
Median – centroid, altitude – orthocenter, angle bisector – incenter, perpendicular bisector – circumcenter
What is the point of concurrency where the altitudes of a triangle intersect?
Orthocenter
Find the equation of a line perpendicular to y = 3x + 1 that passes through the point (2, 5).
y = -1/3x + 19/3 or y - 5 = -1/3(x - 2)