The Incenter Is Equidistant From Each _____ Of A Triangle.

Terms in this set (50)

Original

equidistant

referring to the fact that the distance between two or more points is equal

locus

a set of points whose location is determined by a specific set of conditions

Perpendicular Bisector Theorem

If a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the segment.

Converse of the Perpendicular Bisector Theorem

If a point is equidistant from the endpoints of a line segment, then it lies on the perpendicular bisector of the segment.

Angle Bisector Theorem

If a point is on an angle bisector, it is equidistant from each side of the angle.

Converse of the Angle Bisector Theorem

If a point in the interior of an angle is equidistant from both sides of the angle, then the point lies on the bisector of the angle.

What is the locus of points in a plane that are 3 inches from point A?

A circle with center A and radius 3 inches.

What is the locus of points in three-dimensional space that are 3 inches from point B?

A sphere with center B and radius 3 inches.

What is the locus of points in a plane that are equidistant from endpoints A and B ?

The perpendicular bisector of AB

What is the locus of points equidistant from the sides of ∠ABC?

The angle bisector of ∠ABC

Given: ΔABC;BD↔⊥AC¯;AD¯≅DC¯;BC=7 inches

What is the length of AB¯? 7 inches
By which theorem? Perpendicular Bisector Theorem

Given: ΔABC;BD↔⊥AC¯;AB=BC;AD=5 inches

What is the length of DC¯? 5 inches
By which Theorem? Converse of Perpendicular Bisector Theorem

Given: ΔABC;BD↔⊥AC¯;AB=BC;AC=8 inches

What is the length of AD¯? 4 inches
By which Theorem? Converse of Perpendicular Bisector Theorem

Given: ∠DEF;EI→ bisects ∠DEF;GI=3 in

What is the length of HI? 3 inches
By which Theorem? Angle Bisector Theorem

Given: ∠DEF; point I in the interior of the angle;
m∠DEF=46∘;IG=IH=5 in; IG¯⊥EG¯;IH¯⊥EH¯.

What is the measure of ∠DEI? 23º
By which Theorem? Converse Angle Bisector Theorem

What statement in the Converse of the Angle Bisector Theorem tells you that the point must be in the same plane as the angle?

The point is in the interior of the angle.

circumcenter of a triangle

the point of intersection of the perpendicular bisectors of a triangle

circumscribed circle

a circle that contains a polygon so that it passes through each vertex of the polygon

incenter of a triangle

the point of intersection of the angle bisectors of a triangle

inscribed circle

a circle that is contained within a polygon so that the circle intersects each side of the polygon at exactly one point

Circumcenter Theorem

The circumcenter of a triangle is equidistant from each vertex of the triangle.

Incenter Theorem

The incenter of a triangle is equidistant from each side of a triangle.

The point of intersection of the angle bisectors of a triangle is called the _____ of the triangle.

incenter

The _____ of a triangle is the point of intersection of the perpendicular bisectors of a triangle.

circumcenter

The Incenter Theorem states that the incenter of a triangle is equidistant from each _____ of a triangle.

side

A(n) _____ circle is a circle that is contained within a polygon so that the circle intersects each side of the polygon at exactly one point.

inscribed

The Circumcenter Theorem states that the circumcenter of a triangle is equidistant from each _____.

vertex

A circle that contains a polygon so that it passes through each vertex of the polygon is a(n) _____ circle.

circumscribed

The circumcenter of a right triangle will be on the _____ of the triangle.

hypotenuse

The circumcenter of an obtuse triangle will be in the _____ of the triangle.

exterior

In any triangle, the _____ will always be the same distance from each vertex of the triangle.

circumcenter

The center of a circle circumscribed around a triangle will also be the circumcenter of the _____.

triangle

The center of a circle inscribed in a triangle will also be the _____ of the triangle.

incenter

altitude of a triangle

a segment that extends from the vertex of a triangle to the opposite side and is perpendicular to the side

centroid of a triangle

the point of intersection of the medians of a triangle

median of a triangle

a segment that extends from a vertex of the triangle to the midpoint of the opposite side

orthocenter of a triangle

the point of intersection of all three altitudes of a triangle

Centroid Theorem

The centroid of a triangle is located 2/3 of the distance between the vertex and the midpoint of the opposite side of the triangle along each median.

A segment that extends from the vertex of a triangle to the midpoint of the opposite side is called the _____ of the triangle.

median

The _____ of a triangle is the point of intersection of the medians of a triangle.

centroid

The _____ of a triangle is the point of intersection of the altitudes of a triangle.

orthocenter

A segment that extends from the vertex of a triangle to the opposite side and is perpendicular to the side is called the _____ of the triangle.

altitude

Circumcenters and centroids involve _____.

midpoints

If angles are marked congruent and segments of equal measure extend from the point of intersection to the sides of a triangle, you are dealing with a(n) _____.

incenter

You are dealing with a(n) _____ if a perpendicular segment intersects the side of a triangle at the midpoint.

circumcenter

According to the Centroid Theorem, the _____ of a triangle is located 2/3 of the distance between the vertex and the midpoint of the opposite side of the triangle along each median.

centroid

If there is no indication of congruent or equal segments, you are dealing with a(n) _____.

orthocenter

The orthocenter will lie at the vertex of the right angle in a(n) _____ triangle.

right

The orthocenter will lie in the interior of a(n) _____ triangle.

acute

The orthocenter will lie in the exterior of a(n) _____ triangle.

obtuse