centers of triangles quiz 11/8/19

which point of concurrency are always inside the triangle?

incenter, centroid

the point form which the sculpture will balance was located by finding the intersection point of the ___________ of the triangle.

medians

circumcenter is created by....

perpendicular bisectors

incenter abbreviation

( and brownies if )

orthocenter abbreviation

( at one )

centroid abbreviation

( mom comes )

circumcenter abbreviation

( please bring cookies)

centroid is created by....

Medians

incenter is created by....

angle bisectors

which points of concurrency are always outside of an obtuse triangle?

circumcenter, orthocenter

the three medians of a triangle intersect at a point. which measurements could represent the segments of one of the medians in relation to the point of intersection?

3 cm. and 6 cm.

orthocenter is created by....

Altitudes

a point equally distant form the three sides of a triangle is the intersection of the triangles ____________.

angle bisectors

fido wants to place his dog house equally spaced form a fire hydrant, his favorite tree, and the dirt mound where he buried his favorite bone, as displayed by thr triangle shown at the right. in relation to this triangle, fido should place his dog house _____________________.

at the center of a circumscribed circle.

a test question asks you to inscribe a circle inside of a triangle by construction. which of the following choices is the first step in the construction assuming you are given the triangle?

bisect the angles

which point of concurrency is the center of gravity ( or balance point) of a triangle?

centroid

which point of concurrency is the center of gravity in a triangle?

centroid

which point of concurrency is always on the midpoint of the hypotenuse in a right triangle?

circumcenter

which point of concurrency is equidistant from every vertex?

circumcenter

in a given triangle, the point of intersection of the three altitudes is the same a the point of intersection of the three medians. which type of triangle describes the giving triangle?

equilateral triangle

the incenter is the point forming the origin of a circle ___________ the triangle. the incenter is always inside the triangle. it is constructed by taking the intersection of the ______________________________ of the three vertices of the triangle. the radius of the circle is obtained by dropping a perpendicular from the incenter to any of the triangle legs. it is pictured as the red dashed line. the incenter is the center of the circle such that all three __________ are ____________ form the incenter. to see that the incenter is in fact always inside the triangle, look at an obtuse triangle and a right triangle.

inside, angle bisectors, sides, equidistant.

the centroid of a triangle is constructed by taking any given triangle and connecting the ______________ of each leg of the triangle to the opposite _______________. the line segment created by connecting these points is called the ____________. you see the three medians as the dashed lines in the figure above. no matter what shape your triangle, the ___________ will always be inside the triangle. the centroid is the center of a triangle that can be thought of as the center of mass or the ______________________________ it is the balancing point to use if you want to balance a triangle on the tip of a pencil, for example. the median will be composed of two parts. from the vertex to the centroid and from the centroid to the midpoint. the length from the vertex to the centroid will always be ___________ the length of the __________ and the length from the centroid to the midpoint will always be __________ the length of the ___________.

midpoint, vertex, median, centroid, center of gravity, 2/3, median, 1/3, median.

in which triangle do the three altitudes intersect outside of the triangle?

obtuse triangle

which point of concurrency is always on the vertex of a right triangle?

orthocenter

the orthocenter- the altitude of a triangle is created by dropping a line form each vertex that is ___________________ to the opposite side. an altitude of the triangle is sometimes called the ____________. remember, the altitudes of a triangle do not go through the midpoints of the legs unless you have a special triangle, like an equilateral triangle. like circumcenter, the orthocenter does not have to be inside the triangle. in the obtuse triangle, the orthocenter falls outside the triangle. in a right triangle, the orthocenter falls on a vertex of the triangle.

perpendicular, height

the circumcenter is the center of the circle such that all three ____________ are ______________ from the circumcenter. thus, the ________________ is the point that forms the origin of a circle in which all three vertices of the triangle lie on the circle. the ___________ of the circle is the distance between the circumcenter and any of the triangles three vertices. It is found by finding the _____________________________________ of each leg of the triangle. where all three lines intersect is the ________________. the circumcenter is not always inside the triangle. in fact, it can be outside the triangle, as in the case of an ______________ triangle, or it can fall at the midpoint of the ________________ of a right triangle. see the pictures for examples of this. you can see that even though the circumcenter is outside the triangle in the case of the obtuse triangle, it is still ______________ from all three vertices of the triangle.

vertices, equidistant, circumcenter, radius, perpendicular bisectors, circumcenter, obtuse, hypotenuse, equidistant.