(UNIT 3 - GEOMETRY) INTEGRATED MATH 1 EXAM PREP

What does the notation "m<" mean?

"the measure of an angle"

some facts :

- An angle is formed by two rays that share a common vertex. - Acute angles have measures between 0° and 90°. - Right angles measure 90°. - Obtuse angles have measures between 90° and 180°. - Straight angles measure 180°; they are straight lines; they are formed by opposite rays.

what does the triangle inequality theorem state?

It says that the sum of any two sides of a triangle must be greater than the third side. If not, then there is not enough length for the two sides to meet.

congruent

having the same size and shape; when angles are congruent they have the same measure

Two adjacent, supplementary angles form a(n) _____.

line

parallel lines

lines in the same plane that never intersect

perpendicular lines

lines that intersect to form right (90°) angles

coplanar

lying in the same plane

write, "the measure of angle A is equal to 25 degrees,"

m<A = 25°.

How many diagonals can be drawn from a vertex of an n-gon?

n - 3

Two adjacent angles whose exterior sides are opposite rays are complementary.

never. two opposite rays form a straight line, which is equal to 180 degrees. complementary rays add up to 90 degrees, so opposite rays can never be complementary.

A pair of vertical angles are acute.

sometimes

If angles are supplementary, then one of the angles is an obtuse angle.

sometimes.

If two lines are cut by a transversal, the corresponding angles are equal in measure.

sometimes. they will only be equal in measure if the transversal is intersecting two parallel lines, if it is intersecting perpendicular lines however, the corresponding angles will not be equal in measure.

If a chord passes through the center of the circle, then the chord is called __________________________.

the diameter of the circle

consecutive vertices

the endpoints of one side of a polygon

semicircle

the endpoints of the diameter and all points of a circle lying on one side of the diameter

lateral area

the number of square units in the lateral faces of a three dimensional figure

total area

the number of square units in the surface of a three dimensional figure; also referred to as surface area

legs of a trapezoid

the pair of nonparallel sides in a trapezoid

bases of a trapezoid

the pair of parallel sides in a trapezoid

sector of a circle

the part of a circle bounded by two radii and an arc

sphere

the set of all points in space that are the same distance from a given point, called the center

hypotenuse

the side opposite the right angle in a right triangle

Pythagorean theorem

the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides; a^2 + b^2 = c^2

What does the Pythagorean Theorem state?

the sum of the squares of the legs is equal to the square of the hypotenuse.

names of a polygon

three sides = triangle four sides = square five sides = pentagon six sides = hexagon seven sides - heptagon or septagon eight sides = octagon n sides (the shape isnt complete, some vertices are absent) = n-gon

pyramid

three-dimensional figure whose base is a polygon having its vertices connected to a point, that is not in the same plane, by line segments

prism

three-dimensional figure whose bases are congruent polygons not lying in the same plane with their vertices connected by line segments

adjacent angles

two angles in the same plane that have a common vertex and a common side, but no interior points in common

supplementary angles

two angles with measures that, when added together, equal 180 degrees

complementary angles

two angles with measures that, when added together, equal 90 degrees

what is "is perpendicular to" in symbol form?

⊥

what four requirements must adjacent angles meet?

- They must be in the same plane. - They must have a common vertex. - They must have a common side. - They must have no interior points in common. (They can not overlap.)

A polygon is such that when all diagonals from one vertex are drawn, eleven triangles are formed. How many sides does the polygon have?

13. the amount of triangles that can be formed is always 2 less than the amount of sides the polygon has.

An exterior angle of a regular polygon measures 30 degrees. What is the measure of an interior angle?

150°. 180 - 30 = 150.

The sum of the interior angle measures of a polygon is 2,700°. How many sides does the polygon have?

2,700° = 180°(n - 2) 2,700° = 180°n - 360° 3,060° = 180°n 17 = n The polygon has 17 sides

chord

a line segment whose endpoints lie on a circle

transversal

a line that intersects two or more coplanar lines in different points

theorem

a mathematical statement that can be proven

square

a parallelogram with all angles and all sides congruent

rectangle

a parallelogram with all angles congruent (90°)

rhombus

a parallelogram with all sides congruent

arc

a part of the circumference of a circle

parallelogram

a quadrilateral with both pairs of opposite sides parallel

trapezoid

a quadrilateral with exactly one pair of parallel sides

The sum of the interior angles of a heptagon is _____.

900° you can take 900 + 180 = 1,080 to find the sum of the interior angle for the polygon that has one more additional side. example : triangle : 180 square : 180 + 180 = 360 pentagon : 360 + 180 = 540 hexagon : 540 + 180 = 720 heptagon : 720 + 180 = 900 octagon : 900 + 180 = 1,080 etc. the exception for this is n-gon which is (n-2)180

regular polygon

A polygon that has all of its sides congruent and all of its angles congruent

fact :

For an scalene triangle, the smallest angle will be opposite the shortest side, and the largest angle will be opposite the longest side.

Find the number of sides of a regular polygon if each interior angle measures 150°.

Let n = the number of sides of the polygon. There are 150° in each angle of the regular polygon and all angles are equal. So, there is a total of 150n degrees in the interior angles. 150°n = 180°(n - 2) 150°n = 180°n - 360 °-30°n = -360° n = 12 There are 12 sides in the polygon.

Ray knows that the m<3 = m<6. Which of the following conclusions can Ray make based on the given information?

Lines l and m are parallel because alternate interior angles are equal.

Given the following angles, what ray is the common side of <CFD and <DFE?

Ray FD.

The sum of the interior angles of a polygon, S, having n sides, is given by the formula _____________________.

S = 180°(n - 2)

Every square is a rectangle.

True

diagonal of a polygon

a segment joining two nonconsecutive vertices

cone

a three-dimensional figure consisting of a circle and all points on the circle connected by line segments to a point not in the same plane

cylinder

a three-dimensional figure consisting of two congruent circles, not in the same plane, whose corresponding points are connected by line segments

polyhedron

a three-dimensional figure whose faces are made up of polygons joined at the edges

isosceles trapezoid

a trapezoid with congruent legs

acute triangle

a triangle having all acute angles

right triangle

a triangle that has a right angle

obtuse triangle

a triangle that has one obtuse angle

equiangular triangle

a triangle with all angles equal in measure

equilateral triangle

a triangle with all sides equal in length

isosceles triangle

a triangle with at least two sides equal in length

scalene triangle

a triangle with no two sides equal in length

Find the length of the hypotenuse of a right triangle whose legs are 12 inches and 16 inches.

a^2 + b^2 = c^2 12^2 + 16^2 = c^2 144 + 256 = c^2 400 = c^2 20 = c The hypotenuse is 20 inches long.

<MPR is an acute angle and PQ is in the interior of <MPR. What type of angle is <QPR?

acute angle.

Adjacent angles have no common interior points.

always

central angle

an angle in the plane of a circle with the vertex at the center of the circle

right angle

an angle whose measure equals 90°

straight angle

an angle whose measure is 180°; an angle formed by opposite rays

acute angle

an angle whose measure is greater than zero and less than 90°

obtuse angle

an angle with a measure greater than 90° but less than 180°

major arc

an arc whose degree measure is greater than 180°

minor arc

an arc whose degree measure is less than 180°

if the two legs of a trapezoid are the same length, what do we call it?

an isosceles trapezoid

vertical angles

angles with sides that form two pairs of opposite rays; when two lines intersect, the nonadjacent angles that are formed

polygon

any simple closed figure bounded by three or more segments that only intersect at their endpoints

consecutive sides

any two sides of a polygon that have a common endpoint