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# Discovering Geometry Chapter 5 Conjectures

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The sum of the measures of the four angles of any
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)