geometry
go to the following link: http://image.absoluteastronomy.com/images/encyclopediaimages/t/tr/triangle.centroid.median.png. O is the centroid of ABC. OE = 6, find DE.
(1/3DE = 6; DE = 18) 18
write (a) the inverse and (b) the contrapositive of the statement.if a polygon has eight sides, then it is not an octagon.
(a) if a polygon does not have eight sides, then it is not an octagon. (b) if a polygon is not an an octagon, then it does not have eight sides.
the sum of the measures of the angles of a triangle is
180
the medians of a triangle are concurrent at a point ____ the distance from each _____ to the ____ of the opposite side
2/3; vertex; midpoint
what are concurrent lines?
3 or more lines intersecting in one point
the sum of the measures of the exterior angles of a polygon, one at each vertex, is
360
go to the following link: http://image.absoluteastronomy.com/images/encyclopediaimages/t/tr/triangle.centroid.median.png. O is the centroid of ABC. AE = 12, find OE.
4
consider this triangle: http://2000clicks.com/mathhelp/TriangleABC.gif none of the sides are congruent. which is the largest angle?
B
list the angles in this triangle (http://2000clicks.com/mathhelp/TriangleABC.gif) in order from smallest to largest
B, A, C
T/F a conditional statement and its inverse always have the same truth value.
F
t/f: if a segment is perpendicular to another segment in a triangle, then it must be the bisector.
F
identify the two statements that contradict each other: I. pqr is a right triangle II. pqr is an obtuse triangle III. pqr is scalene
I and II
list triangle congruence theorems/postulates
SAS, SSS, ASA, AAS, HL
T/F: the inverse of a biconditonal is always true.
T
t/f: altitudes can lie outside the triangle
T
if a = b + c and c > 0, then?
a > b
what is the difference between a median and a perpendicular bisector?
a median does not necessarily bisect the segment at a right angle, also it has an endpoint at a vertex
in a right triangle, where is the altitude?
a side
go to textbook page (lib) 260, #15. what is AB?
altitude
What is the negation of the following statement: If an angle is a straight angle, its measure is 180.
an angle is not a straight angle.
the _______ of a triangle are concurrent at a point equidistant from the ______
angle bisectors, sides
exterior angle of a polygon?
angle formed by a side and an extension of the adjacent side
what is an isosceles triangle?
at least two sides congruent
standard form of a linear equation?
ax + by - c
what is it called when a circle is inside a triangle?
circle inscribed in a triangle
what it is called when a triangle is inside a circle?
circle is circumscribed about the triangle
biconditional?
conditional statement with "if and only if"; only if both conditional and converse are true
if a transversal intersects two parallel lines, then alternate exterior angles are
congruent
if a transversal intersects two parallel lines, then alternate interior angles are
congruent
if a transversal intersects two parallel lines, then corresponding angles are
congruent
the statement and the ______ have the same truth value
contrapositive
slopes of parallel lines are
equal
list classifications of a triangle by angle
equiangular, acute, right, obtuse
list classifications of a tirangle by side
equilateral, isosceles, scalene
describe AAS theorem
f two angles and a NONINCLUDED side .....congruent
go to the link: http://www.icoachmath.com/Sitemap/images/Altitude%20of%20a%20Triangle2.jpg which of the images is an altitude?
figure 3
The measure of an exterior angle of a triangle is ______ than the measure of each of its remote interior angles
greater
the sum of the lengths of any two sides of a triangle is _____ ythan the length of third side
greater
concave polygon?
has at least one diagonal with points outside the polygon
law of detachment?
if a conditional is true and its hypothesis is true, then the conclusion is true
triangle midsegment theorem?
if a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length
what is the inverse of the following statement? If a triangle is isosceles, it has two equal sides.
if a triangle is not isosceles, it does not have two equal sides.
state inverse of this statement: if it rains, then they will cancel school
if it does not rain, they will not cancel school
state the converse of this statement: if it rains, then they will cancel school
if they cancel school, it will rain
state the contrapositive of this statement: if it rains, then they will cancel school
if they do not cancel school, it is not raining
describe ASA postulate
if two angles and included side are congruent....congruent triangles
describe SAS postulate
if two sides and included angle are congruent....triangle is congruent
isosceles triangle theorem?
if two sides of a triangle are congruent, then the angles opposite those sides are congruent
point of concurrency of the angle bisectors of a triangle?
incenter of the triangle
in an acute triangle, where is the altitude?
inside the triangle
the converse and the ______ have the same truth value
inverse
if a pt is on the perpendicular bisector of a segment, then
it is equidistant from the endpoints of the segment
if a point is equidistant from the endpoitns of a segment,
it is on the perpendicular bisector of a segment
if two angles of a triangle are not congruent, then teh longer side lies oppose the
larger angle
can a triangle have sides with the given lengths? 2,4,7
no
what is a scalene triangle?
no sides congruent
in an obtuse triangle, where is the altitude?
outside the triangle
f two lines and a transversal form same side interior angles that are supplementary, then the two lines are
parallel
if two liens and a transversal form alternate exterior angles that are congrent, ten the two lines are
parallel
if two lines and a transversal form alternate interior angles that are congruent, then the two lines are
parallel
if two lines and a transversal form corresponding angles that are congruent, then the two lines are
parallel
if two lines and a transversal form same side exterior angles that are supplementary, then the two lines are
parallel
if a segment joins the midpoints of two sides of a triangle, then the segment is _______ to the third side, and is ______ its length
parallel, half
rhombus
parallelogram with four congruent sides
describe the relatioship between a midsegment and the third side of the triangle?
parllel, and half itse length
the ______- of the _____ of a triangle intersect at a point of concurrency equidistant from the vertices
perpendicular bisectors, sides
distance from point to line?
perpendicular distance from point to line
what is the orthocenter of a triangle?
point at which altitudes intersect
what is the point at which concurrent lines intersect?
point of concurrency
circumcenter of a triangle?
point of concurrency of the perpendicular bisectors of a triangle
convex polygon?
polygon with no diagonal with points otuside the polygon
what is an indirect proof?
proof where statement and its negation are only possibilities; and negation is proved wrong
parallelogram
quad with both pairs of opposite sides parallel
what is the median of a triangle?
segment whose endpoints are a vertex and the midpoint of the opposite side
if a transversal intersects two parallel lines, then same side exterior angles are
supplementary
if a transversal intersects two parallel lines, then same side interior angles are
supplementary
if two lines and a transversal form same side exterior angles that are ______, then the two lines are parallel
supplementary
what is the converse of a conditional?
switch of hypothesis and conclusion
If a pt is on the bisector of the angle, then
that point is equidistant from the sides of the angle.
in general, what can be said about the relationshiup between the size of an angle and the length of the opposite side?
the bigger the angle, the bigger the side
if two sides of a triangle are not congruent, then the larger angles lies opposite
the longer side
the perpendicular bisectors of the sides of a triangle intersect at a point of concurrency equidistant from the ______
the perpendicular bisectors of the sides of a triangle intersect at a point of concurrency equidistant from the vertices
what is an altitude of a triangle?
the perpendicular segment from a vertex to the line containing the opposite side (see link: http://www.geogebra.org/en/wiki/images/e/ea/TriangleAltitudePicture.jpg)
if a point is equidistant from the sides of the angle, then
the point is on the bisector of the angle.
what is the centroid?
the point of concurrency of the medians in a triangle
What is the triangle inequality theorem?
the sum of the lengths of any two sides of a triangle is greater than the length of the third side
if two angles of one triangle are congruent to two angles of another triangle , then
the third angles are congruent
the measure of an exterior angle of a polygon is the sum of what two angles?
the two remote interior angles corresponding to the exterior angle
if two lines are parallel to the same line, then
they are parallel to each other
if two lines are perpendicular to the same line, then
they are parallel to each other
concurrent lines?
three or more lines that intersect in the same point
slope intercept form?
y = mx + b
sum of measures of angles of ngon?
(n-2)180
perpendicular lines have a slope product of
-1
find the center of the circle that you can circumscribe about a triangle with vertices (0,0), (-4,0), (0,-6)
-2,-3
point slope form?
y-y1 = m(x-x1)
Find the center of the circle that you can circumscribe aobut the triangle with vertices (0,0), (-8,0), and (0,6)
-4,3
law of syllogism?
if p -> q and q -> r are true statements, then p -> r is a true statement
can a triangle have side with the given lengths? 5, 12, 10
yes
if a condition's symbolic form is p -> q, what is the symbolic form for the negation?
~p
