Geometry Chapter 7 Flashcards

Key Terms in Geometry

• Diagonal: A line segment connecting one vertex of a polygon to another vertex to form a straight line.
• Equilateral Polygon: A polygon where all sides are of equal length.
• Equiangular Polygon: A polygon where all interior angles are congruent.
• Regular Polygon: A polygon that is both equilateral and equiangular.

Types of Quadrilaterals

• Parallelogram: A quadrilateral with at least two pairs of parallel sides.
• Rhombus: A special type of parallelogram with all four sides congruent.
• Rectangle: A parallelogram that includes four right angles.
• Square: A quadrilateral that is a rhombus and also a rectangle, possessing four congruent sides and four right angles.
• Trapezoid: A quadrilateral with exactly one pair of parallel sides.

Properties of Trapezoids

• Bases: The two parallel sides of a trapezoid.
• Base Angles: Angles formed by the base and the legs of the trapezoid.
• Legs: The non-parallel sides of a trapezoid.
• Isosceles Trapezoid: A trapezoid with a line of symmetry between a pair of opposite angles, where the base angles are equal.
• Midsegment: Line segment connecting the midpoints of the legs, parallel to the bases, and its length is half the sum of the base lengths.

Important Theorems

• Theorem 7.1: The sum of the measures of interior angles of a convex n-gon is (n-2) × 180°.
• Corollary 7.1: The interior angles of any quadrilateral sum to 360°.
• Theorem 7.2: The sum of the exterior angles of a convex polygon equals 360°.
• Theorems 7.3 - 7.6: Establish relationships in parallelograms, including that opposite sides and angles are congruent and that diagonals bisect each other.
• Corollary 7.2: A quadrilateral is a rhombus if it has four congruent sides.
• Corollary 7.3: A quadrilateral is a rectangle if it has four right angles.
• Theorem 7.11: A parallelogram is a rhombus if its diagonals are perpendicular.
• Theorem 7.12: A parallelogram is a rhombus if each diagonal bisects a pair of opposite angles.
• Theorem 7.16: A trapezoid is isosceles if and only if its diagonals are congruent.

Specific Properties of Kites

• Kite: A quadrilateral with two distinct pairs of adjacent congruent sides.
• Kite Diagonals: Diagonals are perpendicular, and only one pair of opposite angles is congruent.

Summary of Quadrilateral Properties

• Properties distinguish types of parallelograms (rectangles, rhombuses, squares).
• Criteria for identifying trapezoids and kites through properties such as base angles, diagonals, and sides.