WorksheetsLines, Angles, and Triangles
Total questions: 26
Worksheet time: 52mins
Biconditional
The circle that passes through all vertices (corner points) of a triangle.
statement that can be written in the form “p if and only if q.”
statement that can be written in the form “q if and only if q.”
Contrapositive
“If not p, then not p.”
“If not q, then not p.”
“If not q, then not q.”
ASA triangle Congruence Theorem
If two angles and the included side of one triangle are congruent to three angles and the included side of another triangle, then the triangles are congruent.
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are not congruent.
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
SAS Triangle Congruence Theorem
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
If two sides and the included angle of one triangle are congruent to one sides and the included angle of another triangle, then the triangles are congruent.
If one side and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
SSS Triangle Congruence
If three sides of one triangle are congruent to two sides of another triangle, then the triangles are congruent.
If three sides of one triangle are congruent to one sides of another triangle, then the triangles are congruent.
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
AAS Triangle Congruence
If two angles and an included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent.
If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent.
If two angles and a non-included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent.
HL triangle congruence theorem
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
If the hypotenuse and the legs of a right triangle are congruent to the hypotenuse of another right triangle, then the triangles are congruent.
If the hypotenuse of a right triangle is congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Hypotenuse
In an acute triangle, the side opposite the acute angle.
The two sides that form the sides of the right angle
In a right triangle, the side opposite the right angle.
Legs
The circle that passes through all vertices (corner points) of a triangle.
The two sides that form the sides of the right angle.
The two sides that form the sides of the obtuse angle
Concurrent
when three or more lines intersect at the same point.
The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
statement that can be written in the form “p if and only if q.”
Circumscribed
A circle that contains all the vertices of a polygon.
The point of intersection.
segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side.
Circumcircle
If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle.
inscribed circle
The circle that passes through all vertices (corner points) of a triangle.
Circumcenter
a line segment that connects the midpoints of two sides of the triangle.
The center of the circumcircle of the triangle
The segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is half the length of that side.
Angle Bisector Theorem
A circle that contains all the vertices of a polygon.
The circle that passes through all vertices (corner points) of a triangle.
If a point is on the bisector an of angle, then it is equidistant from the sides of the angle.
Converse of the Angle Bisector Theorem
A circle is inscribed in a polygon if each side of the polygon is tangent to the circle.
If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle.
inscribed circle.
Inscribed
is located at 2/3 of the distance from each vertex to the midpoint of the opposite side.
perpendicular segment from a vertex to the line containing the opposite side.
A circle is inscribed in a polygon if each side of the polygon is tangent to the circle.
Incircle
inscribed circle
A circle is inscribed in a polygon if each side of the polygon is tangent to the circle.
segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side.
Intercenter Theorem
The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side.
is located at 2/3 of the distance from each vertex to the midpoint of the opposite side.
Median
is located at 1/3 of the distance from each vertex to the midpoint of the opposite side.
perpendicular segment from a vertex to the line containing the opposite side.
segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side.
Altitude
inscribed circle
perpendicular segment from a vertex to the line containing the opposite side.
The segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is half the length of that side.
Orthocenter
intersection (or point of concurrency) of the lines that contain the altitudes.
The center of the circumcircle of the triangle.
inscribed circle
Midsegment
when three or more lines intersect at the same point.
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
a line segment that connects the midpoints of two sides of the triangle.
Triangle Midsegment Theorem
The segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is half the length of that side.
In a right triangle, the side opposite the right angle.
The circle that passes through all vertices (corner points) of a triangle.
Point of Concurrency
point of intersection
The perpendicular bisectors of the sides of a triangle intersect at a point that is equidistant from the vertices of the triangle
inscribed circle
Circumcenter Theorem
The two sides that form the sides of the right angle.
A circle that contains all the vertices of a polygon.
The perpendicular bisectors of the sides of a triangle intersect at a point that is equidistant from the vertices of the triangle.
Centroid Theorem
is located at 2/3 of the distance from the opposite side to each vertex.
is located at 1/3 of the distance from each vertex to the midpoint of the opposite side.
is located at 2/3 of the distance from each vertex to the midpoint of the opposite side.
