1 If an animal is a cat, then it makes a “meow” sound.
Parts
» Elementary Geometry for College Students
» TEST 174 Elementary Geometry for College Students
» 4 + 3 ⫽ 7 and an angle has two sides. 2. 4 + 3 ⫽ 7 or an angle has two sides.
» If P, then Qf premises P C. ‹ Q
» If it is raining, then Tim will stay in the house. 2. It is raining.
» If a man lives in London, then he lives in England. 2. William lives in England.
» If P, then Q 2. P If P, then Q If P, then Q P Q
» If an angle is a right angle, then it measures 90°. 2. Angle A is a right angle.
» a Chicago is located in the state of Illinois.
» a Christopher Columbus crossed the Atlantic Ocean.
» If Alice plays, the volleyball team will win. 6. Alice played and the team won.
» The first-place trophy is beautiful. 8. An integer is odd or it is even.
» Matthew is playing shortstop. 10. You will be in trouble if you don’t change your ways.
» If the diagonals of a parallelogram are perpendicular, then
» Corresponding angles are congruent if two parallel lines
» Vertical angles are congruent when two lines intersect. 17. All squares are rectangles.
» Base angles of an isosceles triangle are congruent.
» If a number is divisible by 6, then it is divisible by 3. 20. Rain is wet and snow is cold.
» Rain is wet or snow is cold. 22. If Jim lives in Idaho, then he lives in Boise.
» Triangles are round or circles are square. 24. Triangles are square or circles are round.
» While participating in an Easter egg hunt, Sarah notices
» You walk into your geometry class, look at the teacher,
» Albert knows the rule “If a number is added to each side
» You believe that “Anyone who plays major league
» As a handcuffed man is brought into the police station,
» While judging a science fair project, Mr. Cange finds that
» You know the rule “If a person lives in the Santa Rosa
» As Mrs. Gibson enters the doctor’s waiting room, she
» In the figure, point M is called the midpoint of line
» The two triangles shown are similar to each other.
» Observe but do not measure the following angles.
» Several movies directed by Lawrence Garrison have won
» On Monday, Matt says to you, “Andy hit his little sister at
» While searching for a classroom, Tom stopped at an
» At a friend’s house, you see several food items, including
» If the sum of the measures of two angles is 90°, then these
» If a person attends college, then he or she will be a
» All mathematics teachers have a strange sense of humor.
» If Stewart Powers is elected president, then every family
» If Tabby is meowing, then she is hungry. Tabby is hungry.
» If a person is involved in politics, then that person will be
» If a student is enrolled in a literature course, then he or
» If a person is rich and famous, then he or she is happy.
» If you study hard and hire a tutor, then you will make an
» 1 If an animal is a cat, then it makes a “meow” sound.
» 1 All Boy Scouts serve the United States of America.
» Using the same outer scale, read the angle size by reading the degree
» If line segment AB and line segment CD are drawn to
» How many endpoints does a line segment have? How
» How many lines can be drawn that contain both points A
» Consider noncollinear points A, B, and C. If each line
» Name all the angles in the figure.
» Which of the following measures can an angle have?
» Must two different points be collinear? Must three or
» Which symbols correctly expresses the order in which the
» Which symbols correctly name the angle shown?
» A triangle is named 䉭ABC. Can it also be named 䉭ACB?
» Consider rectangle MNPQ. Can it also be named rectangle
» Suppose ⬔ABC and ⬔DEF have the same measure.
» When two lines cross intersect, they have exactly one
» Judging from the ruler shown not to scale, estimate the
» Judging from the ruler, estimate the measure of each line
» A trapezoid is a four-sided figure that contains one pair of
» An angle is bisected if its two parts have the same Find AC if AB
» Find m ⬔1 if m⬔ABC Find x if m ⬔1
» Find an expression for m ⬔ABC if m⬔1 A compass was used to mark off three congruent
» Use your compass and straightedge to bisect . In the figure, m ⬔1
» Find the bearing of airplane B relative to the control
» Find the bearing of airplane C relative to the control
» Axioms or postulates 4. Theorems
» It is reversible. The definition distinguishes the line segment as a specific part of a line.
» The definition is reversible.
» There exists a number measure for each line segment. 2. Only one measure is permissible.
» Convert 6.25 feet to a measure in inches. 4. Convert 52 inches to a measure in feet and inches.
» Convert meter to feet. 6. Convert 16.4 feet to meters. AB
» In the figure, the 15-mile road
» A cross-country runner jogs at a rate of 15 meters per
» Name three points that appear to be
» How many lines can be drawn through
» Explain the difference, if any, between
» Name two lines that appear to be
» Classify as true or false: Given:
» Can a segment bisect a line? a segment? Can a line bisect
» Suppose that a point C lies in plane X and b point D
» Suppose that a planes M and N intersect, b point A lies
» Suppose that a points A, B, and C are collinear and
» Suppose that points A, R, and V are collinear. If AR
» Using the number line provided, name the point that
» What type of angle is each of the following?
» What relationship, if any, exists between two angles:
» ⬔7 and ⬔8 Suppose that TEST 534
» Must two rays with a common endpoint be coplanar?
» Without using a protractor, name the type of angle
» What, if anything, is wrong with the claim
» ⬔FAC and ⬔CAD are adjacent and
» Using variables x and y, write an equation that expresses
» Using variables x and y, write an equation that expresses Given: m Given: m
» Draw a triangle with three acute angles. Construct angle
» What seems to be true of two of the sides in the triangle
» Refer to the circle with center O. If m If m
» Refer to the circle with center P.
» On the hanging sign, the three angles
» Provide reasons for this proof. “If a Write a proof for: “If a
» Given: ⬔1 ⬵ ⬔3 Given: intersects at
» Given: m Given: Given: Given: Given:
» Given: Triangle ABC TEST 534
» Draw a conclusion based on the results of Exercise 9.
» Given: ⬔s 1 and 3 are complementary
» The Segment-Addition Postulate can be generalized as
» In the proof to the right, provide the missing reasons.
» Construct the Proof. This formal proof is
» If m ⬔1 If two angles are complementary to the same angle, then
» If two lines intersect, the vertical angles formed are
» Any two right angles are congruent. 29. If the exterior sides of two adjacent acute angles form
» If two angles are supplementary to the same angle, then
» If two line segments are congruent, then their midpoints
» If two angles are congruent, then their bisectors separate
» The bisectors of two adjacent supplementary angles form
» The supplement of an acute angle is an obtuse angle.
» Name the four components of a mathematical system. 2. Name three types of reasoning.
» Name the four characteristics of a good definition.
» While watching the pitcher warm up, Phillip thinks, “I’ll
» Laura is away at camp. On the first day, her mother brings
» Sarah knows the rule “A number not 0 divided by itself
» If the diagonals of a trapezoid are equal in length, then the
» The diagonals of a parallelogram are congruent if the
» 1. If a person has a good job, then that person has a
» 1. If the measure of an angle is 90°, then that angle is a
» A, B, and C are three points on a line. AC
» Use three letters to name the angle shown. Also use one
» Figure MNPQ is a rhombus. Draw diagonals and
» Points A, B, C, and D are coplanar. A, B, and C are the
» Line intersects plane X at point P.
» On the basis of appearance, what type of angle is shown? Given: Given:
» Suppose that r is parallel to s
» Does the relation “is parallel to” have a
» In the three-dimensional TEST 534
» If two parallel lines are cut by a transversal, then the
» If a transversal is perpendicular to one of two parallel
» Suppose that two lines are cut by a transversal in such a
» If Matt cleans his room, then he will go to the movie. 2. Matt does not get to go to the movie.
» For each statement in Exercise 9 that can be proved by the
» If lines 艎 and m are not perpendicular, then the angles
» If all sides of a triangle are not congruent, then the
» If no two sides of a quadrilateral figure with four sides
» 1. If the areas of two triangles are not equal, then the two
» 1. If two triangles do not have the same shape, then the
» A periscope uses an indirect method of observation. This
» Some stores use an indirect method of observation. The
» If two angles are not congruent, then these angles are not If , then
» If alternate interior angles are not congruent when two
» If a and b are positive numbers, then .
» In a plane, if two lines are parallel to a third line, then the
» In a plane, if two lines are intersected by a transversal so
» If two lines are parallel to the same line, then these lines
» Explain why the statement in Exercise 33 remains true
» Given that point P does not lie on line 艎, construct the line
» Given that point Q does not lie on , construct the line
» A carpenter drops a plumb line from point A to .
» If two lines are cut by a transversal so that the alternate
» If two lines are cut by a transversal so that the exterior
» Describe the auxiliary line segment as determined,
» a All sides of are of the same length.
» Use an indirect proof to establish the following theorem: Given:
» Given: bisects Given: In rt. ,
» What is the measure of each interior angle
» Consider a polygon of n sides For the concave quadrilateral ABCD,
» Which words have a vertical line of symmetry? Which words have a vertical line of symmetry?
» Complete each figure so that it has symmetry with respect
» Complete each figure so that it reflects across line 艎.
» Complete each figure so that it reflects across line m.
» Suppose that slides to the right to the position of
» Suppose that square RSTV slides point for point to form
» Given that the vertical line is a line of symmetry,
» Given that the horizontal line is a line of symmetry,
» Given that each letter has symmetry with respect to the
» What word is produced by a 180° rotation about the
» What word is produced by a 360° rotation about the
» In which direction clockwise or counterclockwise will
» Considering that the consecutive dials on the electric
» Considering that the consecutive dials on the natural gas
» A regular hexagon is rotated about a centrally located
» A regular octagon is rotated about a centrally located
» Describe the types of symmetry displayed by each of
» Given a figure, which of the following pairs of
» Reflexive Property of Congruence If , then If and
» In the figure for Exercise 2, write a statement that the
» 8. Suppose that you wish to prove that SAS
» Given: and Given that , does it follow that
» Establishing a further relationship, like bisects
» Mark the figures systematically, using:
» Given: and are Given: P Given: Given: and are Given: and Given: and are
» lies in the structural support system of the Ferris Given: In the figure,
» 90° and then 45° 16. 60° and then 30°
» 30° and then 15° 18. 45° and then 105°
» Describe how you would construct an angle
» Construct the complement of the acute
» Construct the right triangle with hypotenuse of length
» Construct a line segment of length 2b. 2. Construct a line segment of length
» Construct a line segment of length . 4. Construct a line segment of length
» Construct an angle that is congruent to acute .
» Construct an angle that is congruent to obtuse .
» Construct an angle that has one-half the measure of .
» Construct an angle that has a measure equal to
» Construct an angle that has twice the measure of .
» Construct an angle whose measure averages the measures
» Construct the triangle that has sides of lengths r and t with
» Construct the triangle that has a side of length t included
» Construct an isosceles triangle with base of length c and
» Construct an isosceles triangle with a vertex angle of 30°
» Construct a right triangle with base angles of 45° and
» Construct the right triangle in which acute angle R has a
» Complete the justification of the construction of the To construct a regular hexagon, what
» Construct an equilateral triangle and its three altitudes. A carpenter has placed a
» One of the angles of an isosceles triangle measures 96°.
» NASA in Huntsville, Alabama at point H, has called a
» Given: Equilateral and TEST 534
» A tornado has just struck a small Kansas community at
» Given: Quadrilateral RSTU with diagonal
» Given: Quadrilateral ABCD with
» In not shown, point Q lies on
» The sides of a triangle have lengths of 4, 6, and x. Write
» The sides of a triangle have lengths of 7, 13, and x. As in
» If the lengths of two sides of a triangle are represented by
» Prove by the indirect method: “The length of a diagonal of
» Prove by the indirect method:
» The length of the median from the vertex of an isosceles
» The length of an altitude of an acute triangle is less than
» ABCD is a parallelogram. Given that ,
» Assuming that in Suppose that diagonals and
» a Which line segment is the a Which line segment is
» In quadrilateral RSTV, the midpoints of consecutive sides ABCD is a parallelogram.
» MNPQ is a parallelogram. Suppose that , MNPQ is a parallelogram. Suppose that ,
» Given that and Given that and
» Given: Parallelogram ABCD with and
» The bisectors of two consecutive angles of are
» When the bisectors of two consecutive angles of a
» Draw parallelogram RSTV with and
» Draw parallelogram RSTV so that the diagonals have
» The following problem is based on the Parallelogram
» In the drawing for Exercise 35, the bearing direction in
» Two streets meet to form an obtuse angle at point B.
» To test the accuracy of the foundation’s measurements,
» For quadrilateral ABCD, the measures of its angles are
» Prove: In a parallelogram, the sum of squares of the
» a As shown, must RSTV be a parallelogram?
» In kite WXYZ, the measures of selected angles are shown.
» In the drawing, suppose that and
» In the drawing, suppose that is the perpendicular
» A carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and
» A carpenter joins four boards of lengths 6 ft, 6 ft, 4 ft, and
» In parallelogram ABCD not shown, , In , In ,
» If the perimeter sum of the lengths of all three sides of
» Given: Kite HJKL with diagonal Given: with diagonals
» Prove that when the midpoints of consecutive sides of a
» If diagonal is congruent to each side of rhombus
» A line segment joins the midpoints of two opposite sides
» If the diagonals of a parallelogram are perpendicular, what
» If the diagonals of a parallelogram are congruent, what
» If the diagonals of a parallelogram are perpendicular and
» If the diagonals of a quadrilateral are perpendicular
» If the diagonals of a rhombus are congruent, what can you
» and R Given: Quadrilateral PQST with midpoints A, B, C, and
» Find the measures of the remaining angles of trapezoid
» What type of quadrilateral is formed when the midpoints
» In trapezoid ABCD, is the median. Without writing a
» Would RSTV have symmetry with respect to
» Given: Isosceles with TEST 534
» In trapezoid RSTV, , TEST 534
» Each vertical section of a suspension bridge is in the
» In trapezoid WXYZ with bases and
» In isosceles trapezoid MNPQ with , diagonal
» In the figure, a b c and B is
» both sides inverted TEST 534
» Assume that AD is the geometric mean of BD and DC in
» All pairs of corresponding sides are proportional. DEFINITION
» a What is true of any pair of corresponding angles of two
» a Are any two quadrilaterals similar?
» a Are any two regular pentagons similar?
» a Are any two equilateral hexagons similar?
» Given , a second triangle Given
» has an inscribed rhombus ARST. If A square with sides of length 2 in. rests as shown on a
» and DF = 3 and and Given: ; ;
» Prove that the line segment joining the midpoints of two with with
» In quadrilateral RSTU, and . Given: is not a right
» In right triangle XYZ, and . Where Diagonal separates pentagon
» Given: , In preparing a certain recipe, a chef uses 5 oz of ingredient
» Given that , are the following proportions true?
» Use Theorem 5.6.1 and the drawing to complete the proof
» In shown in Exercise 27, suppose that
» Given point D in the interior of , suppose that
» Complete the proof of this property:
» Given point D in the interior of
» In right not shown with right
» Use Exercise 33 and the following drawing to complete
» In , the altitudes of the triangle intersect at a point
» In the figure, the angle bisectors of intersect at a
» Given: not shown is isosceles with
» An amusement park ride the “Octopus” has eight Given: Diameters and in
» Given: Circle O with diameter Given: Find if .
» Find if . Is it possible for
» Given: and are Given: Tangents and
» Given: Given: Given: Given: Given: Given: a How are and
» a How are and A quadrilateral RSTV is circumscribed about a circle so
» Given: and are Given: Given: Tangent to at
» Given: with Given: and Given: in Given:
» Sketch two circles that have:
» Two congruent intersecting circles B and D not shown
» For the two circles in Figures a, b, and c, find the
» If a tangent segment and a secant segment are drawn to a
» Construct a circle O and choose some point D on the
» Construct a circle P and choose three points R, S, and T on
» X, Y, and Z are on circle O such
» Construct the two tangent segments to circle P not
» Point V is in the exterior of circle Q not shown such that
» Given circle P and points R-P-T such that R and T are in
» Given parallel chords TEST 534
» In not shown, the length of radius Provide the missing statements and reasons in the
» A circle is inscribed in an isosceles triangle with legs of
» The inscribed circle’s radius is any line segment from the center drawn
» What condition must be satisfied for it to be possible to
» In a regular polygon with each side of length 6.5 cm, the
» If the perimeter of a regular dodecagon 12 sides is
» If the apothem of a square measures 5 cm, find the
» Find the lengths of the apothem and the radius of a square
» Find the lengths of the apothem and the radius of a regular
» Find the lengths of the side and the radius of an
» Find the lengths of the side and the radius of a regular
» Find the measure of the central angle of a regular polygon of
» Find the number of sides of a regular polygon that has a
» Inscribe a regular octagon within a circle. 6. Inscribe an equilateral triangle within a circle.
» Circumscribe a square about a circle. 8. Circumscribe an equilateral triangle about a circle.
» Find the perimeter of a regular octagon if the length of
» Find the measure of each interior angle of a regular
» Find the measure of each exterior angle of a regular
» Find the number of sides for a regular polygon in which
» Is there a regular polygon for which each central angle
» Given regular hexagon ABCDEF with each side of
» Given regular octagon RSTUVWXY with each side of
» Given that RSTVQ is a regular pentagon and is
» Given: Regular pentagon RSTVQ with equilateral
» Given: Regular pentagon JKLMN not shown with
» Prove: If a circle is divided into n congruent arcs
» 14. Consider the information in Exercise 2, but suppose you
» If MNPQ is a rhombus, which formula from this section 17.
» 16. Are and congruent? TEST 534
» is an obtuse triangle with obtuse angle A.
» A square yard is a square with sides 1 yard in length.
» The following problem is based on this theorem: “A
» Gary and Carolyn plan to build the deck shown.
» The roof of the house shown needs to be shingled.
» The exterior wall the gabled
» Carpeting is to be purchased
» A triangular corner of a store has been roped off to be
» Given region R ´ S, explain The algebra method of FOIL multiplication is illustrated Given region
» In the right triangle, find the length of the altitude drawn
» For cyclic quadrilateral ABCD, For cyclic quadrilateral ABCD, find
» Find the ratio of the areas of two similar rectangles if: Given: Equilateral
» Given: Isosceles with Given: In ,
» In a triangle of perimeter 76 in., the length of the first side In a triangle whose area is 72 in
» A trapezoid has an area of 96 cm 14.
» Given: Hexagon RSTVWX with Given: Pentagon ABCDE
» Find the area of a square with
» Find the area of an equilateral triangle with
» Find the area of an equiangular triangle with
» In a regular polygon, each central angle measures 30°. If
» In a regular polygon, each interior angle measures 135°. If
» For a regular hexagon, the length of the apothem is 10 cm.
» For a regular hexagon, the length of the radius is 12 in.
» In a particular type of regular polygon, the length of the
» In one type of regular polygon, the measure of each
» If the area and the perimeter of a regular
» Find the area of a square with apothem and
» Find the area of an equilateral triangle with apothem
» Find the area of an equiangular triangle with apothem
» Find the area of a regular pentagon with an apothem of
» Find the area of a regular octagon with an apothem of
» Find the area of a regular hexagon whose sides have
» Find the approximate area of a regular pentagon whose
» In a regular octagon, the approximate ratio of the length
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