Chapter 4 vocabulary words

dilation

A dilation is a transformation that changes the size of a figure. It can become larger or smaller, but the shape of the figure does not change.

right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).

scalene triangle

A scalene triangle is a triangle that has three unequal sides, such as those illustrated above.

corollary

A statement that follows with little or no proof required from an already proven statement. For example, it is a theorem in geometry that the angles opposite two congruent sides of a triangle are also congruent. A corollary to that statement is that an equilateral triangle is also equiangular.

reflection

A transformation in which a geometric figure is reflected across a line, creating a mirror image. That line is called the axis of reflection.

transformation

A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape. The original shape of the object is called the pre-image and the final shape and position of the object is the image under the transformation.

rigid transformation

A transformation that does not alter the size or shape of a figure; rotations, reflections, translations are all rigid transformations.

corresponding sides of polygons

All pairs of corresponding angles are congruent. 2. The ratios of the measures of corresponding sides are equal.

Acute Triangle

An acute triangle is a triangle with all three angles acute (less than 90°).

equiangular triangle

An equiangular triangle is a triangle where all three interior angles are equal in measure.

remote interior angle

An exterior angle of a triangle, or any polygon, is formed by extending one of the sides of the triangle (or polygon)

isometry

An isometry of the plane is a linear transformation which preserves length.

obtuse triangle

An obtuse triangle is one with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180

interior angle

Any of the four angles formed inside two straight lines when these lines are intersected by a third straight line. An angle formed by two adjacent sides of a polygon and included within the polygon.

CPCTC

Corresponding parts of congruent triangles are congruent" (CPCTC) is a succinct statement of a theorem regarding congruent trigonometry, defined as triangles either of which is an isometry of the other.

vertex of a triangle

Image result for vertex of a triangle definition geometry For polygons, the included angle at each vertex is an interior angle of the polygon. Vertex is also sometimes used to indicate the 'top' or high point of something, such as the vertex of an isosceles triangle , which is the 'top' corner opposite its base, but this is not its strict mathematical definition.

leg of an isosceles triangle

In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base.

translation

Translation is a term used in geometry to describe a function that moves an object a certain distance

exterior angle of a polygon

the angle formed by any side of a polygon and the extension of its adjacent side.

exterior of a polygon

the angle formed by any side of a polygon and the extension of its adjacent side.

corresponding angles of polygons

two nonadjacent angles made by the crossing of two lines by a third line, one angle being interior, the other exterior, and both being on the same side of the third line. ... A general definition is that those triangles are similar in which the corresponding angles are equal.

congruent

(of figures) identical in form; coinciding exactly when superimposed.

triangle rigidity

. A property of triangles that states that if the side lengths of a triangle are fixed, the triangle can have only one shape. included angle. The angle formed by two adjacent sides of a polygon.

base angle of an isosceles triangle

In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles.

vertex angle of an isosceles triangle

In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles.

base of an isosceles triangle

In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles. The vertex opposite the base is called the apex.

isosceles triangle

In geometry, an isosceles triangle is a triangle that has two sides of equal length

base of a triangle

In the case of a triangle, a common way to calculate its area is 'half of base times height' where the 'height' is the altitude, or the perpendicular distance from the base to the opposite vertex. The base can be any side, not just the one drawn at the bottom.

congruent polygons

Polygons are congruent when they have the same number of sides, and all corresponding sides and interior angles are congruent. The polygons will have the same shape and size, but one may be a rotated, or be the mirror image of the other. ... All corresponding interior angles are the same measure.

rotation

Rotation has a central point that stays fixed and everything else moves around that point in a circle.

included side

The common leg of two angles. Usually found in triangles and other polygons, the included side is one that links two angles together.

interior

When we add up the Interior Angle and Exterior Angle we get a straight line 180°. They are "Supplementary Angles".

auxiliary line

adding a line or segment to a proof diagram to help you do the proof. Auxiliary lines often create congruent triangles, or they intersect existing lines at right angles.

equilateral triangle

an equilateral triangle is a triangle in which all three sides are equal.