Chapter 5 Vocabulary - Discovering Geometry

Isosceles Trapezoid Conjecture

• The base angles of an isosceles trapezoid are congruent.
• are supplementary
• A quadrilateral with two pairs of consecutive congruent sides.
• The consecutive angles between the bases of a trapezoid are supplementary.

Isosceles Trapezoid Diagonals Conjecture

• The base angles of an isosceles trapezoid are congruent.
• the number of sides of the polygon
• The diagonals of an isosceles trapezoid are congruent.
• The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal.

Three Midsegments Conjecture

• The three midsegments of a triangle divide the triangle into four congruent triangles.
• A quadrilateral with two pairs of consecutive congruent sides.
• The diagonals of a rectangle are congruent and bisect each other.
• bisects

Triangle Midsegment Conjecture

• The diagonals of a rectangle are congruent and bisect each other.
• A midsegment of a triangle is parallel to the third side and equal to half the length of the third side.
• sometimes true (it is true only if the parallelogram is a rectangle)
• never true

Rectangle Diagonals Conjecture

• sometimes true (only true if the rectangle is a square)
• The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal.
• The diagonals of a rectangle are congruent and bisect each other.
• always true (by the definition of rectangle, all angles are congruent; by the Quadrilateral Sum Conjecture and division, they all measure 90*, so any two angles in a rectangle, including consecutive angles, are supplementary)

Kite Diagonals Conjecture

• sometimes true (only true if the parallelogram is a rectangle; consecutive angles of a parallelogram are always supplementary, but are congruent only if they are right angles)
• are congruent
• The diagonals of a kite are perpendicular to each other.
• 360*

Kite Diagonal Bisector Conjecture

• sometimes true
• sometimes true (only true if the rectangle is a square)
• sometimes true (only true if the rhombus is equiangular)
• The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal.

Trapezoid Consecutive Angles Conjecture

• The consecutive angles between the bases of a trapezoid are supplementary.
• always true (Parallelogram Opposite Angles Conjecture)
• The diagonals of an isosceles trapezoid are congruent.
• always true

Trapezoid Midsegment Conjecture

• are supplementary
• 360*
• sometimes true (only true if the parallelogram is a rectangle; consecutive angles of a parallelogram are always supplementary, but are congruent only if they are right angles)
• The midsegment of a trapezoid is parallel to the bases and equal in length to half the sum of the bases.

Rhombus

• A quadrilateral with two pairs of parallel sides and four congruent sides; an equilateral parallelogram.
• The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal.
• the number of sides of the polygon
• always true (all square fit the definition of rectangle)