Geometry Chapter 11 Flashcards

Questions and Answers

What is Postulate 24 about?

The area of a rectangle

The area of a triangle

The area of a parallelogram

The area of a square (correct)

What does Postulate 25 state?

If two polygons are congruent, then they have the same area.

What is the Area Addition Postulate?

The area of a region is the sum of the areas of its nonoverlapping parts.

What does Theorem 11.1 provide information about?

The area of a rectangle is the product of its base and height. Signup and view all the answers

What is the definition of the base of a parallelogram?

Either pair of parallel sides of a parallelogram. Signup and view all the answers

How is the height of a parallelogram defined?

The perpendicular distance between the bases of a parallelogram. Signup and view all the answers

What does Theorem 11.2 state regarding parallelograms?

The area of a parallelogram is the product of a base and its corresponding height. Signup and view all the answers

What is Theorem 11.3 about?

The area of a triangle is one half the product of a base and its corresponding height. Signup and view all the answers

How is height defined in relation to a trapezoid?

The perpendicular distance between the bases of a trapezoid. Signup and view all the answers

What does Theorem 11.4 state about trapezoids?

The area of a trapezoid is one half the product of the height and the sum of the lengths of the bases. Signup and view all the answers

What does Theorem 11.5 highlight about rhombuses?

The area of a rhombus is one half the product of the lengths of its diagonals. Signup and view all the answers

What does Theorem 11.6 explain about kites?

The area of a kite is one half the product of the lengths of its diagonals. Signup and view all the answers

What relationship is described by Theorem 11.7?

If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a^2:b^2. Signup and view all the answers

Define circumference.

The distance around a circle. Signup and view all the answers

What does Theorem 11.8 define?

The circumference C of a circle is C = 3.14(d) or C = 2(3.14)r. Signup and view all the answers

What is meant by arc length?

A portion of the circumference of a circle. Signup and view all the answers

What does the Arc Length Corollary state?

In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360 degrees. Signup and view all the answers

What is Theorem 11.9 related to circles?

The area of a circle is 3.14 times the square of the radius. Signup and view all the answers

What is Theorem 11.10 about?

The ratio of the area of a sector of a circle to the area of the whole circle is equal to the ratio of the measure of the intercepted arc to 360. Signup and view all the answers

What defines the sector of a circle?

The region bounded by two radii of the circle and their intercepted arc. Signup and view all the answers

What does Theorem 11.11 state about regular polygons?

The area of a regular n-gon with side length S is one half the product of the apothem A and the perimeter P. Signup and view all the answers

What is the radius of a polygon?

The radius of a polygon's circumscribed circle. Signup and view all the answers

Define the apothem of a polygon.

The distance from the center to any side of the polygon. Signup and view all the answers

What is a central angle of a regular polygon?

An angle formed by two radii drawn to consecutive vertices of the polygon. Signup and view all the answers

What is probability?

A measure of the likelihood that the event will occur. Signup and view all the answers

What does geometric probability involve?

A ratio that involves a geometric measure such as length or area. Signup and view all the answers

Study Notes

Area Postulates and Theorems

Area of a Square Postulate: Area is the square of the side length.
Area Congruence Postulate: Congruent polygons have equal areas.
Area Addition Postulate: Total area equals the sum of nonoverlapping areas.

Area of Common Shapes

Area of a Rectangle: Calculated as the product of base and height (A = base × height).
Area of a Parallelogram: Given by A = b × h, where b is the base and h is the height.
Area of a Triangle: Computed as A = 1/2 × base × height.
Area of a Trapezoid: A = 1/2 × height × (base1 + base2).
Area of a Rhombus: A = 1/2 × d1 × d2, with d1 and d2 being the diagonals.
Area of a Kite: Also A = 1/2 × d1 × d2.

Areas of Similar Polygons

Similar polygons have areas in the ratio of the squares of their corresponding sides (a^2:b^2).

Circle Measurements

Circumference: The distance around a circle, calculated as C = πd or C = 2πr.
Arc Length: A portion of the circumference.
Arc Length Corollary: The length of an arc compared to the full circumference is proportional to the measure of the arc over 360 degrees.

Area of a Circle and Sector

Area of a Circle: A = πr², where r is the radius.
Area of a Sector: The area ratio is equivalent to the intercepted arc measure over 360 degrees.

Regular Polygons

Area of a Regular Polygon: Calculated as A = 1/2 × apothem × perimeter (A = 1/2aP), where P is the perimeter and A is the apothem.
Radius of the Polygon: Refers to the radius of the circumscribed circle.
Apothem: The distance from the center to a side of the polygon.

Geometry and Probability

Probability: Indicates the likelihood of an event occurring.
Geometric Probability: Involves a ratio that relates to geometric measurements like area or length.

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Description

Explore key concepts from Geometry Chapter 11 with these flashcards. This quiz covers important postulates regarding area and congruence, including Postulates 24, 25, and 26. Test your understanding of geometric principles with concise definitions and theorems.