Geometry Chapter 7 Flashcards

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Questions and Answers

What is the definition of a diagonal?

A line connecting two adjacent vertices

A line perpendicular to a side

A line from one vertex to the opposite corner (correct)

A line that bisects the angles

What describes an equilateral polygon?

All sides are equal

What defines an equiangular polygon?

All angles are congruent

What is a regular polygon?

Equilateral and equiangular Signup and view all the answers

What is a parallelogram?

A shape with two or more parallel sides Signup and view all the answers

What is a rhombus?

A parallelogram with four congruent sides Signup and view all the answers

How is a rectangle defined?

A parallelogram with four right angles Signup and view all the answers

What is a square?

A parallelogram with four congruent sides and four right angles Signup and view all the answers

What describes a trapezoid?

A quadrilateral with only one pair of parallel sides Signup and view all the answers

What is meant by 'bases' in geometry?

Surface that holds up a shape Signup and view all the answers

What are base angles?

Angles at the bases of shapes Signup and view all the answers

What are legs in geometry?

Sides Signup and view all the answers

What characterizes an isosceles trapezoid?

Line of symmetry bisecting a pair of opposite angles Signup and view all the answers

What is the midsegment of a trapezoid?

Parallel to each base and 1/2 the sum of the bases Signup and view all the answers

What defines a kite in geometry?

Two pairs of congruent sides Signup and view all the answers

What is Theorem 7.1 concerning polygon interior angles?

The sum of the measures of the interior angles of a convex n-gon is (n-2) x 180 Signup and view all the answers

What does Corollary 7.1 state?

The sum of the measures of the interior angles of a quadrilateral is 360° Signup and view all the answers

What does Theorem 7.2 state about polygon exterior angles?

The sum of the measures of exterior angles of a convex polygon is 360° Signup and view all the answers

What is Theorem 7.3 regarding parallelograms?

If a quadrilateral is a parallelogram, then its opposite sides are congruent Signup and view all the answers

What does Theorem 7.4 state about a parallelogram's opposite angles?

If a quadrilateral is a parallelogram, then its opposite angles are congruent Signup and view all the answers

What does Theorem 7.5 state about consecutive angles in a parallelogram?

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary Signup and view all the answers

What is established by Theorem 7.6?

If a quadrilateral is a parallelogram, then its diagonals bisect each other Signup and view all the answers

What does Theorem 7.7 state about opposite sides of a quadrilateral?

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram Signup and view all the answers

According to Theorem 7.8, what can be said about pairs of opposite angles in a parallelogram?

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Signup and view all the answers

What does Theorem 7.9 explain about opposite sides in a parallelogram?

If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram Signup and view all the answers

What does Theorem 7.10 imply about quadrilaterals?

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram Signup and view all the answers

What is Corollary 7.2 regarding rhombuses?

A quadrilateral is a rhombus if and only if it has four congruent sides Signup and view all the answers

What does Corollary 7.4 state about squares?

A quadrilateral is a square if and only if it is a rhombus and a rectangle Signup and view all the answers

What is the criteria for rectangles according to Corollary 7.3?

A quadrilateral is a rectangle if and only if it has four right angles Signup and view all the answers

What statement does Theorem 7.11 make about rhombuses and diagonals?

A parallelogram is a rhombus if and only if its diagonals are perpendicular Signup and view all the answers

What can be said about a rhombus regarding its diagonals according to Theorem 7.12?

A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles Signup and view all the answers

What does Theorem 7.13 indicate about rectangles and their diagonals?

A parallelogram is a rectangle if and only if its diagonals are congruent Signup and view all the answers

What does Theorem 7.14 state about isosceles trapezoids?

If a trapezoid is isosceles, then each pair of base angles is congruent Signup and view all the answers

What is the converse of the isosceles trapezoid base angles?

If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid Signup and view all the answers

What does Theorem 7.16 stipulate about isosceles trapezoids?

A trapezoid is isosceles if and only if its diagonals are congruent Signup and view all the answers

What does Theorem 7.17 say about trapezoids and midsegments?

The midsegment of a trapezoid is parallel to each base, and its length is 1/2 the sum of the lengths of the bases Signup and view all the answers

What is stated by Theorem 7.18 regarding kites?

If a quadrilateral is a kite, then its diagonals are perpendicular Signup and view all the answers

What does Theorem 7.19 explain about the opposite angles in a kite?

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent Signup and view all the answers

Study Notes

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.

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Prepare to master Geometry with these flashcards from Chapter 7 of Big Ideas Math. Each card features essential terms and definitions, helping you to deepen your understanding of geometric concepts like diagonals and polygon types. Perfect for studying or quick review before a test.