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WHS geometry
1st semester
80
Mathematics
9th Grade
11/25/2012

Additional Mathematics Flashcards

 


 

Cards

Term

Distance Formula

or

Length of a segment

having endpoints

(x1 , y1 ) and ( x2 , y2 )

Definition
[image]
Term
Supplementary angles
Definition
2 angles which have a sum of 180°
Term
Complementary Angles
Definition
2 angles having a sum of 90°
Term
Linear pair
Definition

adjacent supplementary angles

 

[image]

Term
Triangle Angle Sum Theorem
Definition
The angles of a triangle have a sum of 180°
Term
Midsegment of a triangle
Definition

1.  has endpoints which are the midpoints of two sides

2.  is parallel to the third side of the triangle

3.  has a length half of the third side

 

2(length of midsegment) = length of third side

Term
Exterior angle theorem
Definition

The measure of the exterior angle of a triangle is equal to the sum of the two remote interior angles.

 

 

 

[image]

Term

perpendicular

 

_l_

Definition

intersect to form right angles

 

Term
parallel lines
Definition

equal slopes

never intersect

coplanar

Term
Reflexive
Definition

Any value is equal to itself.

Any figure is congruent to it.

 

3=3

AB≅AB

 

Term
altitude
Definition
The segment from the vertex of a triangle, perpendicular to the opposite side.

Also called the height.

The intersection of the three altitudes of a triangle is called the ORTHOCENTER.
Term
Orthocenter
Definition
The intersection of the three altitudes of a triangle.
Term
incenter
Definition
The intersection of the three angle bisectors of a triangle.

To inscribe a circle in a triangle, you must first construct at least two angle bisectors then construct a perpendicular from the incenter to a side.
Term
Circumcenter
Definition
The intersection of the three perpendicular bisectors of a triangle.

To circumscribe a circle around a triangle, you must first construct at least two perpendicular bisectors of the sides, then use the distance from the circumcenter to a vertex as the radius of your circle.
Term

If two sides of a triangle are known, how do you find the possible range of values for the third side?

 

Let two sides be x and y.

x>y

Definition
The missing third side is between the difference and sum of the two given sides.

The third side is between (x-y) and (x+y)

The third side is greater than (x-y) and less than (x+y)

(x-y) < missing side < (x+y)
Term

How can you determine if three segments lengths can form a triangle?

 

Let the three sides be x,y, and z.

The smallest values are x and y.

Definition
The sum of the two smallest side lengths must be more than the third side length.

x + y > z

(Cannot be equal or less)
Term
Symmetric
Definition

If a=b then b=a

If m<ABC= 40°, then 40° = m<ABC.

Term
Transitive
Definition
If a=b and b=c, then a=c
Term

Midpoint of a segment having endpoints

(x1, y1)(x2, y2)

Definition

x1 +x2    ,    y1 + y2

   2                 2    

 

Term

Slope "m" of the line containing two given points

(x1, y1 ) and (x2, Y2)

Definition

y2 -y1

x2-x1

 

Term
parallel lines
Definition

Parallel lines are coplanar and do not intersect.

 

Parallel lines have same slope "m" in the equations

y=mx+b

and y-y1 = m(x-x1)

Term
Perpendicular lines
Definition

The slopes of perpendicular lines are opposite reciprocals.

 

If one is 2/3, the other is  -3/2


The product of the slopes of perpendicular lines = -1

 

2-3 = -1

 3     2        

Term
conditional
Definition

If p, then q

 

p→q

Term
converse
Definition

If q, then p

 

q→p

Term
inverse
Definition
  ̴p  →      ̴q
Term
contrapositive
Definition

  ̴q   →       ̴p

 

The contrapositive has the same truth value as the original conditional.

Term
Syllogism
Definition

p→ q, q→ r, p→ r

 

If p, then q.  If q, then r. 

 If p, then r.

Term
Detachment
Definition

p→q

p

_______

∴q


It does not work backwards.

p→q

q

_______

no conclusion possible

Term
Perpendicular Bisector
Definition
a segment, ray , line or plane that intersects a segment at its midpoint at a right angle
Term
acute
Definition
an angle with degree measure less than 90°
Term
obtuse
Definition
an angle with degree measure between 90° and 180°
Term
straight angle
Definition
an angle with measure 180°
Term
opposite rays
Definition

two rays with the same endpoint which are collinear

 

<----•-----------------•------------------•---->

A                      B                        C

 

ray BA  and ray BC are opposite rays.

Term
alternate interior angles
Definition

if two parallel lines are cut by a transversal, the alternate interior angles are congruent.

[image]

m∠5=m∠6         and       m∠7= m∠8    

Term
same-side interior angles
Definition

If two parallel lines are cut by a transversal, the same-side interior angles are supplementry and have a sum of 180°.    

 

[image]

 

 

Term
Corresponding angles
Definition

If two parallel lines are cut by a transversal the corresponding angles are congruent (equal). [image]

Term

[image]

 

List the sides of the triangle in increasing order.

Definition
RS, RQ, QS
Term

[image]

 

List the angles in decreasing order.

Definition
<P, <M, <N
Term

[image]

 

What is the possible range of values for s?

 

Definition

7-4 < s < 7+4

 

3<s<11

 

 

 

 

 

Term
same-side exterior angles
Definition

If two parallel lines are cut by a transversal, same-side exterior angles are supplementary.

 

[image]

a+b=180

Term
alternate exterior angles
Definition

[image]

If two parallel lines are cut by a transversal, alternate interior angles are congruent.

<1=<8  and  <2=<7

Term
Centroid
Definition

The intersection of the three medians of a triangle.

[image]

Term
construct an angle bisector
Definition
http://www.hstutorials.net/math/geometry/constructions/bisect_acute_angle.htm[image]
Term
Construct the Perpendicular Bisector
Definition
http://www.hstutorials.net/math/geometry/constructions/perp_bisector.htm[image]
Term
Vertical Angles
Definition
[image]
Term
Ruler postulate
Definition

1. used to find the length of a segment on a number line

2.  if the endpoints are A and B

the length of AB = l A-B l

3.  Absolute value will produce a positive answer.

Term
Adjacent Angles
Definition

share a common side and a common vertex, but no common interior points.

[image]

Term
construct a perpendicular from a point not on a line
Definition

http://www.hstutorials.net/math/geometry/constructions/perpendicular_not_on_line.htm

 

 

 [image]

Term
hypothesis
Definition
p
Term
Median of a triangle
Definition
The median is the segment from the vertex of a triangle to the midpoint of the opposite side.[image]
Term
Biconditional
Definition

p  ↔  q

p if and only if q

Term
What is the formula to find the sum of all the interior angles of a convex polygon with "n" sides?
Definition

180(n-2)

or

180(#sides - 2)

Term
conclusion
Definition
q
Term
SSS congruency of triangles
Definition
[image][image]
Term
ASA congruency of triangles
Definition
[image][image][image]
Term
SAS congruency of triangles
Definition
[image][image]
Term
What is the sum of the exterior angles of a convex polygon?
Definition
360°
Term
What is the formula to find the measure of one exterior angle of a regular convex polygon, if you know how many sides it has?
Definition

360/#sides

or

360÷sides

Term
What is the formula to determine how many sides a regular polygon has, if you know the measure of an exterior angle?
Definition

360/ext. angle

or

360÷(measure of one exterior angle)

Term
Diagonal
Definition
[image]A segment connecting two non-consecutive vertices of a polygon.
Term
parallelogram
Definition
A quadrilateral with 2 pairs of opposite parallel sides
Term
Opposite sides of a parallelogram are__?__
Definition
parallel and congruent
Term
Opposite angles of a parallelogram are__?__
Definition
congruent
Term
2 consecutive angles of a parallelogram are _?_
Definition

Supplementary

add up to equal 180

Term
The diagonals of a parallelogram  __?__
Definition
bisect each other.
Term
The diagonals of a rectangle are__?__
Definition
Congruent    [image]
Term

Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle, and the included angle of one is less than the included angle of the other, then the third side of the first triangle is shorter than the third side of the second triangle.

Definition
[image]
Term
The diagonals of a rhombus are __?__
Definition

perpendicular

and

bisect opposite angles

[image]

Term
Rhombus
Definition

A parallelogram with 4 congruent sides.

 

The diagonals of a rhombus are perpendicular.

 

The diagonals of a rhombus bisect the opposite angles.

 

Term
midsegment of a trapezoid
Definition

[image]

MN is the midsegment. 

 M and N are the midpoints of the legs.

MN is parallel to AD and BC.

MN =½(AD + BC)

Term
When a rhombus is given one diagonal, what type of triangles are formed?
Definition
2 congruent isosceles triangles
Term
When both diagonals are drawn in a rhombus, the four triangles formed are __?__
Definition
congruent right triangles
Term
[image]
Definition
E.
Term

formula to find arc length in terms of [image], if you know the degree measure of the central angle m° and radius r of the intercepted arc.

 

Definition

( 2 [image] r ) 

360           

Term
Sector area formula
Definition

( [image] r2 )

360          

Term
equation of a circle with center (h,k) and radius r
Definition
(x-h)2 + (y-k)2 = r2
Term
how to find chord lengths in a circle
Definition
[image]
Term
AAS conguency
Definition
Term
HL congruency
Definition
Term
Equation of a Circle
Definition
(x-h)2+ (y-k)2=r2
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