Discovering Geometry Chapter 5 Conjectures

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Quadrilateral Sum Conjecture

The sum of the measures of the four angles of any
quadrilateral is 360°. (Lesson 5.1)

Pentagon Sum Conjecture

The sum of the measures of the five angles of any pentagon is 540°. (Lesson 5.1)

Polygon Sum Conjecture

The sum of the measures of the n interior angles of an n-gon is 180°(n - 2). (Lesson 5.1)

Exterior Angle Sum Conjecture

For any polygon, the sum of the measures of a set of exterior angles is 360°. (Lesson 5.2)

Equiangular Polygon Conjecture

You can find the measure of each interior angle of an equiangular n-gon by using either of these formulas: 180 - (360/n) or (180(n - 2))/n. (Lesson 5.2)
360°

Kite Angles Conjecture

The nonvertex angles of a kite are congruent. (Lesson 5.3)

Kite Diagonals Conjecture

The diagonals of a kite are perpendicular. (Lesson 5.3)

Kite Diagonal Bisector Conjecture

The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal. (Lesson 5.3)

Kite Angle Bisector Conjecture

The vertex angles of a kite are bisected by a diagonal. (Lesson 5.3)

Trapezoid Consecutive Angles Conjecture

The consecutive angles between the bases of a trapezoid are supplementary. (Lesson 5.3)

Isosceles Trapezoid Conjecture

The base angles of an isosceles trapezoid are congruent. (Lesson 5.3)

Isosceles Trapezoid Diagonals Conjecture

The diagonals of an isosceles trapezoid are congruent. (Lesson 5.3)

Three Midsegments Conjecture

The three midsegments of a triangle divide it into four congruent triangles. (Lesson 5.4)

Triangle Midsegment Conjecture

A midsegment of a triangle is parallel to the third side and half the length of the third side. (Lesson 5.4)

Trapezoid Midsegment Conjecture

The midsegment of a trapezoid is parallel to the bases and is equal in length to the average of the lengths of the bases. (Lesson 5.4)

Parallelogram Opposite Angles Conjecture

The opposite angles of a parallelogram are congruent. (Lesson 5.5)

Parallelogram Consecutive Angles Conjecture

The consecutive angles of a parallelogram are supplementary. (Lesson 5.5)

Parallelogram Opposite Sides Conjecture

The opposite sides of a parallelogram are congruent. (Lesson 5.5)

Parallelogram Diagonals Conjecture

The diagonals of a parallelogram bisect each other. (Lesson 5.5)

Double-Edged Straightedge Conjecture

If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart as the first pair, then the parallelogram formed is a rhombus. (Lesson 5.6)

Rhombus Diagonals Conjecture

The diagonals of a rhombus are perpendicular, and they bisect each other. (Lesson 5.6)

Rhombus Angles Conjecture

The diagonals of a rhombus bisect the angles of the rhombus. (Lesson 5.6)

Rectangle Diagonals Conjecture

The diagonals of a rectangle are congruent and bisect each other. (Lesson 5.6)

Square Diagonals Conjecture

The diagonals of a square are congruent, perpendicular, and bisect each other. (Lesson 5.6)

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