Basic Geometry - Ch.7 Theorems Flashcards
What is the sum of the measures of the interior angles of an n-sided convex polygon?
(n - 2) ∙ 180°
What is the sum of the measures of the exterior angles of a convex polygon?
360°
If a quadrilateral is a parallelogram, what can be said about its opposite sides?
Opposite sides are congruent
If a quadrilateral is a parallelogram, what can be said about its opposite angles?
Opposite angles are congruent
If a quadrilateral is a parallelogram, what can be said about its consecutive angles?
Consecutive angles are supplementary
If a parallelogram has one right angle, what can be concluded about its angles?
It has four right angles
If a quadrilateral is a parallelogram, what can be said about its diagonals?
Diagonals bisect each other
If a quadrilateral is a parallelogram, what does each diagonal do?
Separates the parallelogram into two congruent triangles
What condition must be met for a quadrilateral to be a parallelogram regarding one pair of opposite sides?
Both parallel and congruent
If a parallelogram is a rectangle, what can be said about its diagonals?
Diagonals are congruent
If a parallelogram is a rhombus, what can be said about its diagonals?
Diagonals are perpendicular
If a parallelogram is a rhombus, what do its diagonals do to a pair of opposite angles?
Each diagonal bisects a pair of opposite angles
What can be concluded if the diagonals of a parallelogram are perpendicular?
The parallelogram is a rhombus
If one diagonal of a parallelogram bisects a pair of opposite angles, what can be concluded?
The parallelogram is a rhombus
If two consecutive sides of a parallelogram are congruent, what can be concluded?
The parallelogram is a rhombus
If a quadrilateral is both a rectangle and a rhombus, what is it?
A square
If a trapezoid is isosceles, what can be said about each pair of base angles?
Each pair of base angles is congruent
How can a trapezoid be identified as isosceles in relation to its diagonals?
Its diagonals are congruent
What does the midsegment of a trapezoid do?
Is parallel to each base and its length is one half the sum of the lengths of its bases
If a quadrilateral is a kite, what can be said about its diagonals?
Diagonals are perpendicular
If a quadrilateral is a kite, what can be said about its opposite angles?
Exactly one pair of opposite angles are congruent
