# 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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