Geometry Topic 1 Transformations and Congruence Vocabulary Point

Geometry Topic 1 Transformations and Congruence

Vocabulary

Point – a point has no dimension. It is a location on a plane. It is represented by a dot. Line – a line has one dimension. It is an infinite set of points represented by a line with two arrowheads that extends without end. Line segment – a line segment consists of two endpoints and all the points between them. Plane – a plane has two dimensions extending without end. It is often represented by a parallelogram. Ray – a ray has one endpoint and extends without end in one direction. Note: Name the endpoint first. BC and CB are different rays.

Coplanar – points that lie in the same plane. Collinear – points that lie on the same line. Midpoint - divides a segment into two congruent segments. K, L and M are collinear points. Segment bisector – a line, ray or segment that divides a segment into two congruent segments. Angle – a figure forms by two rays with a common endpoint. Vertex – the common endpoint of two or more rays or line segments.

Side of an angle – one of the two rays that form an angle. Angle bisector – a ray that divides an angle into two congruent angles. Perpendicular lines – lines that intersect at 90° angles. Perpendicular bisector - a segment, ray, line, or plane that is perpendicular to a segment at its midpoint. Linear pair – a pair of adjacent angles whose non-common sides are opposite rays or share one common side. Parallel lines – lines in the same plane that do not intersect.

Transformation – a change in the position, size, or shape of a figure. A transformation maps the preimage to the image. Translation - a transformation in which all the points of a figure move the same distance in the same direction; the figure is moved along a vector so that all of the segments joining a point and its image are congruent and parallel. Rigid motion– a transformation of the plane or space, which preserves distance and angles. Reflection – a transformation across a line, called the line of reflection. The line of reflection is the perpendicular bisector of each segment joining a point and its image.

Rotation – a transformation about a point P, also known as the center of rotation, such that each point and its image are the same distance from P. All of the angles with vertex P formed by a point and its image are congruent. Center of rotation – the point around which a figure is rotated. Pre-image A has been transformed by a 90° clockwise rotation about the point (2, 0) to form image A’. Pre-image has been transformed by a 90° clockwise rotation about the origin. Symmetry – the transformation of a figure such that the image coincides with the preimage, the image and preimage have symmetry. Line of Symmetry – a line that divides a place figure into two congruent reflected halves.

Rotational symmetry – a figure that can be rotated about a point by an angle less than 360° so that the image coincides with the preimage has a rotational symmetry. Complementary angles – two angles whose measures have a sum of 90°. Supplementary angles – two angles whose measures have a sum of 180°.

Topic 2 Lines, Angles, and Triangles

Vocabulary

Vertical angles – the non adjacent angles formed by two intersecting lines. Transversal – a line that intersects at least two other lines. Hypotenuse – the side opposite the right angle in a right triangle. Line t is a transversal. Interior angle – an angle formed by two sides of a polygon with a common vertex. Exterior angle – an angle formed by one side of a polygon and the extension of an adjacent side. Auxiliary line – a line drawn in a figure to aid in a proof.

Parallel Lines

Isosceles triangle – a triangle with at least two congruent sides. Equilateral triangle – a triangle with three congruent sides. Triangle Inequality Theorem - The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Equiangular triangle – a triangle with three congruent angles. Example: AB + BC > AC AC + BC > AB AB + AC > BC

Congruent Triangles SSS Triangle Congruence Postulate SAS Triangle Congruence Postulate

ASA Triangle Congruence Postulate AAS Triangle Congruence Theorem HL Right Triangle Congruence

Topic 3 Lines, Angles, and Triangles – Part B

Vocabulary

Equidistant – the same distance from two or more objects. Distance from a point to a line – the length of the perpendicular segment from the point to the line. Median of a triangle – a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. Midsegment of a triangle – a segment that joins the midpoints of two sides of the triangle. • • • The midsegment is always parallel to the third side of the triangle. The midsegment is always half the length of the third side. A triangle has three possible midsegments, depending on which pair of sides is initially joined.

Circumscribed circle – every vertex of the polygon lies on the circle. Point of concurrency – a point where three or more lines coincide. Inscribed circle – a circle in which each side of the polygon is tangent to the circle. Altitude of a triangle – a segment from a vertex perpendicular to the opposite side. P Vocabulary for Geometry Honors

Circumcenter of a triangle – the point of concurrency of the three perpendicular bisectors of a triangle. Centroid of triangle – the point of concurrency of the three medians of a triangle. Also known as the center of gravity. § The circumcenter is also the center of the triangle's circumcircle - the circle that passes through all three of the triangle's vertices. § The circumcenter is equidistant from all three vertices of the triangle. § In the special case of a right triangle, the circumcenter lies exactly at the midpoint of the hypotenuse. § The centroid is always inside the triangle § Each median divides the triangle into two smaller triangles of equal area. § The centroid is exactly two-thirds the way along each median. § The centroid divides each median into two segments whose lengths are in the ratio 2: 1, with the longest one nearest the vertex. Incenter of a triangle – the point of concurrency of the three angle bisectors of a triangle. § The incenter is the center of the triangle's incircle, the largest circle that will fit inside the triangle and touch all three sides. § The triangle's incenter is always inside the triangle.