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Glencoe mathematics geometry
ch. 1-6 review
48
Mathematics
10th Grade
01/22/2009

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Cards

Term

Distance formula

Definition
d=√(x2-x1)2+(y2-y1)
Term
slope formula
Definition

slope= rise/run

or

y2-y1/x2-x1

 

Term
midpoint formula
Definition
m= (x1+x2/2), (y1+y2/2)
Term
slope intercept form
Definition
y=mx+b
Term
point-slope form
Definition
y-y1=m(x-x1)
Term
segment addition postulate
Definition
if B is between A and C, then AB+BC= AC
Term
Conditional statement
Definition

formed by given hypothesis and concusion

sybol p→q.

Example: if two angles have the same measure, then they are congruent.

Term
Converse Statement
Definition

exchanging th hypothesis and conclusion of the conditional.

symbol: q→p.

Example: If two angles are congruent, then they have the same measure.

Term
Inverse Statement
Definition

Negating both the hypothesis and conclusion of the conditional.

Symbol: not p→not q

example: If two angles do not have the same measure, then they are not congruent.

 

Term
Contrapositive
Definition

negating both the hypothesis and conclusion of the converse statement.

symbol: not q→not p.

Example: If two angles are not congruent, then they do not have the same measures.

Term
Angle Adddition Postulate
Definition
if R is in the interior of <PQS, then m<PQR + m<RQS= m<PQS
Term
Definition
Angles supplementary to the same angle or to congruent angles are congruent.
Term
Definition
Angles complementary to the same angle or to congruent angles are congruent.
Term
Definition
perpendicular lines intersect to form four right angles
Term
Definition
All right angles are congruent
Term
Definition
Perpendicular lines form congruent adjacent angles
Term
Definition
If two angles are congruent and supplementary, then each angle is a right angle
Term
Definition
If two congruent angles form a linear pair, then they are right angles.
Term
Perpendicular Transversal Therom
Definition
In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendiular to the other.
Term
Angle Sum Theorem
Definition
The sum of the measures of the angles of a triangle is 180 degrees.
Term
Third Angle Theorem
Definition
If two angles of one triangle are congruent to two angles of a second triangle then the third angles of the triangles are congruent.
Term
Exterior Angle Theorem
Definition
The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles.
Term

Side and Angle triangle congruence

Definition
SSS, SAS, AAS, ASA
Term
Congruence in right triangles
Definition

LL- leg leg congruence

HA- Hypotenuse angle congruence

LA- Leg angle congruence

HL- hypotenuse leg congruence

Term
Isosceles triangle theorem
Definition
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
Term
Converse of Isosceles Triangle Theorem
Definition

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Term
Circumcenter Theorem
Definition
The circumcenter of a triangle is equidistant from all vertices of a triangle
Term
Angle Bisector Theorems
Definition
  • Any point on the angle bisector is equidistant from the sides of the angle.
  • Any point equidistant from the sides of an angle lies on the angle bisector
Term
Median
Definition

segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex on the median.

point of concurrency: Centroid

Term
Centroid Theorem
Definition
The centroid of a triangle is located 2/3 if the distance from a vertex to the midpoint of the side opposite the vertex on a median.
Term
Altitude
Definition

segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side.

point of concurrency: orthocenter

Term
Exterior Angle Inequality Theorem
Definition

If an angle is an exterior angle of a triangle, then its measure is greater then the measure of either of its corresponding remote interior angles.

Term
Definition

If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.

Term
Definition
If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
Term
Triangle Inequality Theorem
Definition

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Term
Corollary
Definition
the perpendicular segment from a point to a plane is the shortest segment from the point to the plane.
Term

Side and Angle Triangle Inequality

Definition
SAS, SSS
Term
Side and Angle similarity
Definition
SSS, SAS, AA
Term
Triangle Proportionality Theorem
Definition
If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it seperates these sides into segments of proportional lengths.
Term
Converse of Triangle Proportionality Theorem
Definition
If a line intersects two sides of a triangle and seperates the sides into corresponding segments of proportional lengths, then the line parallel to the third side
Term
Triangle Midsegment Theorem
Definition
A midsegment of a triangle is parallel to one side of a triangle and its length is 1/2 length of that side.
Term
Three parallel lines cut by a transversal theorem (1)
Definition
If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.
Term

Three parallel lines cut by a transversal corollary (2)

Definition
If three or more parallel lines cut off congruent segments on one transversal, they cut off congruent segments on all transversals.
Term
Special Segments on Similar Triangles
Definition
  • Similar triangles have corresponding altitudes proportional to corresponding sides.
  • Similar triangles have corresponding angle bisectors proportional to corresponding sides.
  • Similar triangles have corresponding medians proportional to corresponding sides.
Term
Proportional Perimeter Theorem
Definition

If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides.

Term

Angle Bisector Theorem

Definition
An angle bisector in a triangle seperates the opposite side into segments that have the same ratio as the other two sides.
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