Geometry Review Flashcards

Flashcards for geometry vocabulary and theorems.

Diagonal

A segment that connects any two nonconsecutive vertices of a polygon.

Parallelogram

A quadrilateral with both pairs of opposite sides parallel.

Rectangle

A parallelogram with four right angles.

Rhombus

A parallelogram with all four sides congruent.

Square

A parallelogram with four congruent sides and four right angles.

Trapezoid

A quadrilateral with exactly one pair of parallel sides; the parallel sides are called bases and the nonparallel sides are called legs.

Isosceles Trapezoid

A trapezoid with congruent legs.

Midsegment of a Trapezoid

The segment that connects the midpoints of the legs of a trapezoid.

Kite

A quadrilateral with exactly two pairs of consecutive congruent sides.

Polygon Interior Angles Sum Theorem

The sum of the interior angles of an n-sided convex polygon is (n-2)180.

Polygon Exterior Angles Sum Theorem

The sum of the exterior angles of an n-sided convex polygon, one angle at each vertex, is 360.

Parallelogram Opposite Sides Theorem

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Parallelogram Opposite Angles Theorem

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Parallelogram Consecutive Angles Theorem

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Parallelogram Right Angle Theorem

If a parallelogram has one right angle, then it has four right angles.

Parallelogram Diagonals Bisect Theorem

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Opposite Sides Congruent Parallelogram Converse

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Opposite Angles Congruent Parallelogram Converse

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Diagonals Bisect Parallelogram Converse

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

One Pair Opposite Sides Congruent & Parallel Parallelogram Converse

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

Rectangle Diagonals Theorem

If a parallelogram is a rectangle then its diagonals are congruent.

Rectangle Diagonals Converse Theorem

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Rhombus Diagonals Perpendicular Theorem

If a parallelogram is a rhombus, then its diagonals are perpendicular.

Rhombus Diagonals Bisect Angles Theorem

If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

Rhombus Diagonals Perpendicular Converse

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Rhombus Diagonal Bisects Angles Converse

If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.

Rhombus Consecutive Sides Congruent

If one pair of consecutive sides of a parallelogram are congruent, the parallelogram is a rhombus.

Rectangle and Rhombus Quadrilateral

If a quadrilateral is both a rectangle and a rhombus, then it is a square.

Isosceles Trapezoid Base Angles Theorem

If a trapezoid is isosceles, then each pair of base angles is congruent.

Isosceles Trapezoid Base Angles Converse

If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid.

Isosceles Trapezoid Diagonals

A trapezoid is isosceles if and only if its diagonals are congruent.

Trapezoid Midsegment Theorem

The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases.

Kite Diagonals Theorem

If a quadrilateral is a kite, then its diagonals are perpendicular.

Kite Opposite Angles Theorem

If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.

Ratio

A comparison of two quantities using division.

Extended Ratios

Used to compare three or more quantities. (a:b:c means a:b, b:c, and a:c are ratios).

Proportion

An equation stating that two ratios are equal.

Means and Extremes

In the proportion a/b = c/d, the numbers a and d are called __, and the numbers b and c are called __.

Cross Products

The product of the extremes and the product of the means.

Similar Polygons

Polygons that have the same shape but not necessarily the same size.

Scale Factor

The ratio of the lengths of the corresponding sides of two similar polygons.

Midsegment of a Triangle

A segment with endpoints that are the midpoints of two sides of the triangle.

Perimeters of Similar Polygons Theorem

If two polygons are similar, then their perimeters are proportional to the scale factor between them.

Angle-Angle Similarity (AA~)

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Side-Side-Side Similarity (SSS~)

If the corresponding side lengths of two triangles are proportional, then the triangles are similar.

Side-Angle-Side Similarity (SAS~)

If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.

Reflexive Property of Similarity

ΔABC ~ ΔABC.

Symmetric Property of Similarity

If ΔABC ~ ΔDEF, then ΔDEF ~ ΔABC.

Transitive Property of Similarity

If ΔABC ~ ΔDEF, and ΔDEF ~ ΔXYZ, then ΔABC ~ ΔXYZ.

Similar Triangles Altitudes Theorem

If two triangles are similar, the lengths of corresponding altitudes are proportional to the lengths of corresponding sides.

Similar Triangles Angle Bisectors Theorem

If two triangles are similar, the lengths of corresponding angle bisectors are proportional to the lengths of corresponding sides.

Similar Triangles Medians Theorem

If two triangles are similar, the lengths of corresponding medians are proportional to the lengths of corresponding sides.

Pythagorean Triple

A set of three nonzero whole numbers a, b, and c such that a2+b2=c2.

Trigonometry

The study of the properties of triangles and trigonometric functions and their applications.

Trigonometric Ratio

A ratio of the lengths of sides of a right triangle.

Sine

For an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the hypotenuse.

Cosine

For an acute angle of a right triangle, the ratio of the measure of the leg adjacent to the acute angle to the measure of the hypotenuse.

Tangent

For an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the leg adjacent to the acute angle.

Inverse Sine

The inverse function of sine, or sin-1. If the sine of an acute ∠A is equal to x, then sin-1x is equal to the measure of ∠A.

Inverse Cosine

The inverse function of cosine, or cos-1. If the cosine of an acute ∠A is equal to x, then cos-1x is equal to the measure of ∠A.

Inverse Tangent

The inverse function of tangent, or tan-1. If the tangent of an acute ∠A is equal to x, then tan-1x is equal to the measure of ∠A.

Angle of Elevation

The angle between the line of sight and the horizontal when an observer looks upward.

Angle of Depression

The angle between the line of sight and the horizontal when an observer looks downward.

Circle

The locus or set of all points in a plane equidistant from a given point called the center of the circle.

Radius

A segment with endpoints at the center and on the circle.

Chord

A segment with endpoints on the circle.

Diameter

A chord that passes through the center and is made up of collinear radii.

Concentric Circles

Coplanar circles that have the same center.

Circumference

The distance around the circle.

Inscribed Polygon

A polygon is _ in a circle if all of its vertices lie on the circle.

Circumscribed Circle

A circle is _ about a polygon if it contains all the vertices of the polygon.

Central Angle

An angle with a vertex in the center of the circle.

Arc

A portion of a circle defined by two endpoints.

Minor Arc

The shortest arc connecting two endpoints on a circle.

Major Arc

The longest arc connecting two endpoints on a circle.

Semicircle

An arc with endpoints that lie on a diameter.

Congruent Arcs

Arcs in the same or congruent circles that have the same measure.

Adjacent Arcs

Arcs in a circle that have exactly one point in common.

Arc Length

The distance between endpoints along an arc measured in linear units.

Inscribed Angle

An angle has a vertex on a circle and sides that contain chords of the circle.

Intercepted Arc

An arc has endpoints on the sides of an inscribed angle and lies in the interior of the inscribed angle.

Tangent

A line in the same plane as a circle that intersects the circle in exactly one point called the point of tangency.

Common Tangent

A line, ray or segment that is tangent to two circles in the same plane.

Secant

A line that intersects a circle in exactly two points.

Chord Segments

The segments each chord is divided into when two chords intersect inside a circle.

Secant Segment

A segment of a secant line that has exactly one endpoint on the circle.

External Secant Segment

A secant segment that lies in the exterior of the circle.

Tangent Segment

A segment of the tangent with one endpoint on the circle.

Arc Addition Postulate

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Arc Central Angle Congruence Theorem

In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent.

Arc Chord Congruence Theorem

In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Diameter Chord Bisector Theorem

If a diameter or radius of a circle is perpendicular to a chord, then it bisects the chord and its arc.

Perpendicular Bisector of Chord Theorem

The perpendicular bisector of a chord is a diameter or radius of a circle.

Chord Distance to Center Theorem

In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

Inscribed Angle Theorem

If an angle is inscribed in a circle, then the measure of the angle equals ½ the measure of its intercepted arc.

Inscribed Angles Intercepting Same Arc Theorem

If two inscribed angles of a circle intercept the same arc or congruent arcs, then the angles are congruent.

Inscribed Angle Diameter Theorem

An inscribed angle of a triangle intercepts a diameter or semicircle if and only if the angle is a right angle.

Inscribed Quadrilateral Theorem

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

Tangent Radius Theorem

In a plane, a line is tangent to a circle if and only if it is perpendicular to a radius drawn to the point of tangency.

Tangent Segments Theorem

If two segments from the same exterior point are tangent to a circle, then they are congruent.