Geometry Basics
What does “collinear” mean?
Points that lie on the same straight line.
A conjunction is true when…
Both statements are true
∠1 and ∠8 are what type of angles?
Alternate exterior
Slope of (-4, –13) to (8, 5).
3/2
Check if 6, 10, 14 can be triangle sides.
Yes (6 + 10 > 14)
What does “coplanar” mean?
Points that lie on the same plane.
Truth value: p ∧ q, where p = true (“Dallas is in Texas”), q = false (“All birds can fly”).
False
If ℓ ∥ m and m∠1 = 52°, find m∠5.
52° (corresponding)
Lines with slopes –2 and 1/2.
Parallel, perpendicular, or neither?
Perpendicular
If ΔABC ≅ ΔDEF and AB = 5y – 3, DE = 119, solve for y.
y = 24.4 (if using the diagram’s actual numbers)
What does a “midpoint” do to a segment?
It divides the segment into two congruent parts.
Converse of “If two angles are adjacent, then they form a linear pair.”
“If two angles form a linear pair, then they are adjacent.”
q ∥ r: Solve (8x + 1) = (21x + 5).
x = –4/13
Write a line parallel to y = –2x + 8 through (–1, –3).
y = –2x – 5
Which congruence method: right triangles with hypotenuse and one leg congruent?
HL
If the endpoints of segment AB are A(–1, 7) and B(11, –1), what is the length formula you would use to find AB?
The Distance Formula.
Which law?
Given: If the kicker makes the field goal → team wins.
Given: If the team wins → they go to playoffs.
Conclusion: If kicker makes the field goal → they go to playoffs.
Law of Syllogism
Converse used to prove a ∥ c if m∠3 = m∠9.
Alternate Interior Angles Converse
Slope of the vertical line through x = –2.
Undefined
If ΔCDE ~ ΔHFG and CD = 4x-1 and CE = x+5, GH = 4 and FH = 10, solve for CD.
CD = 35
A segment has midpoint (2, –7) and one endpoint at (8, –5). What process do you use to find the other endpoint?
Set up the midpoint formula and solve for the missing coordinates.
Property: If JK + KL = MN + KL, then JK = MN.
Subtraction Property of Equality
If q||r, solve for x if these two angles are alternate exterior. m<1 = 7x -10 and m<2 = 9x-44
x=17
Write a line perpendicular to 4x – 3y = 15 through (8, –5). *leave in point-slope form*
y + 5 = (3/4)(x – 8)
For ΔRST with angles 64°, 57°, and 59°, order sides greatest → least.
Opposite 64°, opposite 59°, opposite 57°