Geometry Leap Flashcards
(22 cards)
How do you construct:
Line congruent to another one
Perpendicular bisector
Perpendicular bisector through a point on a line
Perpendicular bisector through a point off a line
Angle congruent to another one
Angle bisector
Parallel lines
Equilateral trianlge
Equilateral triangle inside a circle
Hexagon
Square inside a circle
Tell me how to classify triangles based on their angles, and based on their side lengths.
What are skew lines?
Lines in different planes that do not interesect and are not parallel to each other.
Explain all 3 rigid transformations
Explain rotational and reflectional symmetry
What lines with transversals are supplementary?
Linear pair, Same side interior
Say the congruence theorems for triangles
Say the strategies for proofs
Draw the parallelograms and their properties:
Rectangle, square, rhombus, parallellogram, Kite, trapezoid
Explain dilations
What are the triangle congruence theorems
What is an altitude/height?
How can you find it?
What does it do to a triangle?
Explain the leg rule for the similar triangles (the ratio. - it’s easier than you think).
How do you add, subtract, multiply, divide, simplify, and rationalize square roots?
WHAT ARE THE SPECIAL RIGHT TRIANGLES?
WHAT ARE THEIR SIDE PROPERTIES?
DRAW THIS OUT!!!
45-45-90 - X, X, X√2
30-60-90 - X√3, X, 2X
Explain cofunctions, inverse operations, and Angle of elevation,depression.
Lateral surface area vs. Total SA
Rule of K for area and volu,e
Proof of pi r squared
Explain cross sections
Rule for the dilation of general cones
Say the formula for doing this, and the idea
It is that, if you make a cross section in a cone that is parallel to the base, you will get a similar cone.
The rule for this is: ACS/B = (LH/BH)^2 = (SF)^2
Base/height
Cavalieri’s Principle
General Cone cross section Theorem
You know about the base and height.
Cavalieri’s Principle - If 2 solids have the same height and coplanar Cross-sectional area at every level, they have teh same volume.
General cone corss sectoin theorem - If 2 general cones have he same base, height, and the cross sections are the same distance from the base, the cross sections all have the same are.a.
Explain and draw the DMV
What are:
Distance formula
Pythagorean theorem
Circle equation/Radius equation
General form of circle equation, and completing the square, using (X^2-6x-9) as an example
Midpoint formula
Perpendicular line property
Thale’s theorem
Explain the tips for remembering these.
D^2: ((X2-X1)^2) + (Y2-Y1)^2)
A^2+B^2=C^2
(x - h)² + (y - k)² = r²
Explain general form ane complete the square, using x² + y² + 4x - 6y - 3 = 0 as an example
M = ((x1 + x2)/2, (y1 + y2)/2)
Explain perpendicular line property.
Explain Thale’s theorem.
Explain the shoelace method.
Go right ahead, explain
WHAT ARE:
Circumcenter
Incenter
Centroid
Orthocenter
Euler’s line
Explain the tips for remembering these.
Circumcenter: Intersection of all perpendicular bisectors
Incenter: Intersection of all angle bisectors
Centroid: Intersection of medians
Orthocenter: Intersection of heights/altitudes
Euler’s Line: Line that connects orthocenter, circumenter, and centroid
Explain the rules for:
Central Angle
Inscribed Angle
Interior angle
Exterior angle
Parts of interior angles in circles
Tangent-secant side length property
2 Secant property
Secant-tangent on the circle’s edge arc makes?
Radius-Tangent
2Tangents that meet at the same point, converse
Perpendicular diameter and chord, converse
Intercepted arcs by congruent chord, converse
Central angle formed by congruent chords, converse
cyclic quadrilaterals
Circle parts
Radians vs. Degrees, and all that’s related
Explain:
OR: mutually exclusive and inclusive
AND: Inclusive and non-inclusive
Conditonal probability theorem
What all of this means
P(A or B) = P(A) + P(B)
P(A or B) = P(A) + P(B) - P(A and B)
P (A and B) = P(A) * P(B)
P (A and B) = P(A) * P(B|A)
Conditional probability - P(A|B) = P (A and B) / P(B)
