Shapes and Curves in Geometry

A closed two-dimensional shape formed by straight line segments.

A line segment connecting two non-adjacent vertices of a polygon.

A polygon with three sides and three angles.

A polygon with four sides and four angles.

A polygon with five sides and five angles.

A polygon with six sides and six angles.

Polygons are categorized by the number of their sides.

A polygon with n sides.

An angle that measures between 0° and 90°.

An angle that measures between 90° and 180°.

An angle that measures between 180° and 360°.

A polygon where all interior angles are less than 180° and all diagonals lie inside the polygon.

A polygon with at least one interior angle greater than 180° and some diagonals outside the polygon.

A polygon with all sides equal in length and all angles equal in measure.

A polygon where not all sides or angles are equal.

Regular polygons have all sides and all angles equal. Irregular polygons do not have all sides or all angles equal.

A quadrilateral with one pair of parallel sides.

Two angles that add up to 180 degrees.

The angles formed inside a trapezium by the intersection of a transversal and the parallel sides.

A quadrilateral with two pairs of adjacent sides equal in length.

Sides of a polygon that share a common vertex.

A kite has the following properties: 1) Two pairs of adjacent sides are equal in length. 2) The diagonals are perpendicular bisectors of each other.

A line segment that divides a line segment into two equal parts.

A line segment that cuts another line segment in half at a 90-degree angle.

A quadrilateral with two pairs of parallel sides. Opposite sides and angles are equal.

Angles formed when a transversal intersects two parallel lines. They are on the inside of the parallel lines and on opposite sides of the transversal, and they are congruent.

Triangles that have the same size and shape, with corresponding sides and angles being equal.

Two triangles are congruent if two angles and the included side are equal.

The sides of a parallelogram that are across from each other. They are always equal in length.

The diagonals of a parallelogram bisect each other. This means they cut each other in half at the point of intersection.

To prove triangles congruent, you need to establish that corresponding sides and angles are equal. Use congruency theorems like ASA (Angle-Side-Angle)

When triangles are congruent, corresponding sides and angles are equal. Identify these matching parts to prove congruency.

A quadrilateral with opposite sides parallel and equal in length, and opposite angles equal.

A parallelogram with four right angles.

A parallelogram with all sides equal in length.

A quadrilateral with four equal sides and four right angles.

A square has four equal sides and four right angles.

The line segments that connect opposite vertices of a parallelogram. These diagonals bisect each other, meaning they cut each other in half at their point of intersection.

A kite is a quadrilateral with two pairs of adjacent sides equal in length. Its diagonals are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other into two equal parts.

In a kite, the opposite angles that are between the sides of unequal length are equal. This means the two angles that are not adjacent to each other across the longer diagonal are equal.

A quadrilateral with one pair of parallel sides. These sides are called the bases, and the other two sides are called the legs.

Two or more lines that lie in the same plane and never intersect, no matter how far they extend. They have the same direction and slope.

In a parallelogram, opposite angles are equal. This means the angles across from each other are congruent.

A parallelogram has several properties: 1) Opposite sides are parallel and equal. 2) Opposite angles are equal. 3) Diagonals bisect each other. 4) Consecutive angles are supplementary (add up to 180 degrees).