Fennels Flashcards
Parallelogram
A quadrilateral with two pairs of parallel sides
Lel
If parallelogram, then…
- opposite side are congruent
- opposite angles congruent
- diagonals bisect each other
- consecutive angles are supplementary
If ____________, then parallelogram.
- one pair of opposite sides are parallel and congruent
- both pairs of opposite sides are congruent
- both pairs of opposite angles are congruent
- an angle is supplementary to both consecutive angles
- diagonals bisect each other
If rectangle, then…
- qualities of a parallelogram
- diagonals are congruent
- angles are right
If ____________, then rectangle.
- one angle is right
- diagonals are congruent and bisect each other
If rhombus, then…
- qualities of a parallelogram
- all sides are congruent
- diagonals are perpendicular
- diagonals bisect opposite angles
If ____________, then rhombus.
- one pair of consecutive sides is congruent
- diagonals are perpendicular
- one diagonal bisects opposite angles
Polygon Angle Sum Theorem
The sum of the interior angles of a convex polygon with (n) sides is 180(n-2) degrees.
Polygon Exterior Angle Sum Theorem
The sum of the exterior angle measures of a convex polygon is 360 degrees.
If square, then…
- qualities of a rhombus
- qualities of a rectangle
- diagonals create 4 congruent isosceles right triangles
If kite, then…
- diagonals are perpendicular
- exactly one pair of opposite angles is congruent
- two pairs of adjacent sides are congruent (all sides are NOT congruent)
If isosceles trapezoid, then…
- bases parallel
- legs congruent
- each pair of base angles is congruent
- diagonals are congruent
If trapezoid and ____________, then isosceles trapezoid.
- one pair of base angles is congruent
- diagonals are congruent
- legs congruent
Trapezoid Midsegment Theorem
The length of the midsegment of a trapezoid is half the sum of the base’s lengths.
Perimeters of Similar Polygons
If two polygons are similar, then their perimeters are proportional to the scale factor between them.
SSS Similarity
If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
SAS Similarity
If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.
Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides into segments of proportional lengths.
Converse of Triangle Proportionality Theorem
If a line intersects two sides of a triangle and separates the sides into proportional corresponding segments, then the line is parallel to the third side of the triangle.
Triangle Midsegment Theorem
A midsegment of a triangle is parallel to one side of the triangle, and its length is one half of the length of that side.
If similar triangles, then…
-lengths of corresponding altitudes, angle bisectors, and medians are proportional to lengths of corresponding sides
Triangle Angle Bisector
Separates the opposite side into two segments that are proportional to the lengths of the other two sides.
Congruent Arcs
In the same or congruent circles, two minor arcs are congruent if and only if their central angles/corresponding chords are congruent.
If the radius or diameter of a circle is perpendicular to a chord…
…then it bisects the chord and arc.
What is the perpendicular bisector of a chord?
The diameter.
Congruent Chords
In the same or congruent circles, two chords are congruent if and only if they are equidistant from the center.
If a quadrilateral is inscribed in a circle…
…then the opposite angles are supplementary.
Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the two adjacent arcs.
If three or more parallel lines intersect two transversals…
…then they cut off the transversals proportionally.
If three or more parallel lines cut off congruent segments on one transversal…
…then they cut off congruent segments on every transversal.
What are the proportions of the sides of a 30-60-90 triangle?
x, 2x, x(root3)
What are the proportions of the sides of a 45-45-90 triangle?
x, x, x(root2)
Concentric Circles
Two coplanar circles with the same center
Annulus
The region between two concentric circles
Apothem
A segment from the center of a polygon perpendicular to a side
Chord
A segment joining two points on a circle
Secant
A line that intersects a circle at two points
Arc
A piece of a circle; measure is in degrees
AA Similarity (Postulate)
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Inscribed Polygon
Inside a circle & touching as many points as possible without overlapping it. The radius of the circle = the radius of the polygon.
Circumscribed Polygon
Outside a circle & touching as many points as possible without cutting into it. The radius of the circle = the apothem of the polygon.
Common Tangent
A line tangent to two circles
Semicircle
An arc whose endpoints are the points of the diameter
Tangent
A line that intersects a circle once, perpendicular to the radius
What is special about an angle inscribed in a semicircle?
It will always be right.
If two lines are cut by a transversal such that __________, then they are parallel.
If parallel lines are crossed by a transversal, then __________.
- AIAs are congruent
- AEAs are congruent
- Corresponding angles are congruent
- CIAs are supp
- CEAs are supp
If two coplanar lines are both perpendicular to a third line…
…then they are parallel.
What 4 things determine a plane?
- 3 noncollinear points
- A line & a point not on the line
- Two intersecting lines
- Two parallel lines
What is a foot?
The point of intersection between a plane and a line not on the plane.
What are skew lines?
Two lines that are not coplanar.
What is the sum of the measures of the angles of a triangle?
180 degrees.
The measure of an exterior angle of a triangle is equal to what?
The sum of the measures of the remote interior angles.
Midline Theorem
A segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.
No-Choice Theorem
If two angles of one triangle are congruent to two angles of another, then the third angles are congruent.
Parallel Postulate
Given a line and a point not on the line, there is exactly one line through the point parallel to the line.
What is the equation for the number of diagonals that can be drawn in a polygon?
n(n-3)/2
Identify the geometric mean of this proportion: 1/4 = 4/16
4
What is dilation? What is reduction?
Dilation is when a figure is enlarged, and reduction is when a figure is shrunk. In both cases, the sides of the resulting figure will be proportional to the sides of the original figure, and the two figures will be similar.
AA Theorem
If two corresponding angles of a triangle are congruent, then the triangles are similar.
List the ways triangles can be proven congruent.
- SSS
- ASA
- SAS
- AAS (side not included)
- HL (if right triangles)
