Which term best defines the type of reasoning used below Abdul broke out in hives the last four times that he ate chocolate candy Abdul concludes that he will break out in hives if he eats chocolate ID: 674648
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Slide1
GEOMETRY FINAL REVIEW-ch.2
Which term best defines the type of reasoning used below? “Abdul broke out in hives the last four times that he ate chocolate candy. Abdul concludes that he will break out in hives if he eats chocolate.” InductiveDeductiveConverseInverse
a) InductiveSlide2
GEOMETRY FINAL REVIEW-ch.3
LJ and GH are parallel and m< L = 40°.Find the measures of the numbered angles.m< 1 = ______ m< 2 = ______
m< 3 = ______
ANSWER:
m< 1 = 100° m< 2 = 40°m< 3 = 140°Slide3
GEOMETRY FINAL REVIEW-ch.3
In the figure below, m<3 + m<5 = 180°. Determine which lines are parallel. Justify your reasoning.
Line
r
is parallel to line
s.Justifications may vary. One approach to justification: converse of same side interior angles theoremSlide4
GEOMETRY FINAL REVIEW-ch. 2
The given statement is a valid geometric proposition. Statement: If a triangle has two congruent angles, then it is an isosceles triangle. a) Write the contrapositive of this statement: b) NOW, Determine if the contrapositive statement is valid. Explain your reasoning.
a) If a triangle is not isosceles, then the triangle does not have two angles that are congruent
.
b)
The contrapositive statement is valid. The triangle could be equilateral, which is also isosceles. It could also be scalene, with no congruent angles. Also, the contrapositive of a true statement is always true. If a statement is false, its contrapositive
will be false also. Slide5
GEOMETRY FINAL REVIEW-ch.
2The given statement is a valid geometric proposition.Statement: If a quadrilateral is a kite, then its diagonals are perpendicular. Which of the following is the inverse statement?a) If a quadrilateral has diagonals that are perpendicular, then it is a kite.b) If a quadrilateral is not a kite, then its diagonals are not perpendicular. c) If a quadrilateral has diagonals that are not perpendicular, then it is not a kite.
d) If a quadrilateral is a kite, then its diagonals are not perpendicular
BSlide6
GEOMETRY FINAL REVIEW-ch.
5Which is the correct construction of a perpendicular bisector of AB?CSlide7
GEOMETRY FINAL REVIEW-ch.
3Which is the correct construction of a line segment parallel to AB passing through point C?CSlide8
GEOMETRY FINAL REVIEW-ch.1
Complete the following statements. a) The ceiling and floor of your kitchen are examples of __________planes. b) A wall and the floor of your kitchen are examples of _____________planes. Word choices: CoplanarParallel Skew Perpendicular
Parallel
PerpendicularSlide9
GEOMETRY FINAL REVIEW-ch.1
Complete the following statement: Two lines that do not lie in the same plane are called ________________ lines. a) Coplanarb) Parallelc) Skew d) PerpendicularCSlide10
GEOMETRY FINAL REVIEW-ch. 5
In ΔABC, point I is the incenter. m < BAI = x + 4 m < IAC = 2x – 6
Find the value of
x.
x=10Slide11
GEOMETRY FINAL REVIEW-ch. 5
ΔLPT is an obtuse scalene triangle. If P is the obtuse angle in the triangle, which of the following is not a valid conclusion?a) m< L + m T < m <Pb) m< L + m <T < 90°c) m< L + m< T = 90° d) m < L + m < T + m < P = 180°
CSlide12
GEOMETRY FINAL REVIEW-ch. 5
Which triangle has an altitude that is also a median? Slide13
GEOMETRY FINAL REVIEW
In the diagram below, <E ≅ <D and AE ≅ CD. Prove AB ≅ CB using mathematical language and concepts. One approach to the justification: <E ≅ <D and AE ≅ CD
Given
<
ABE
≅<CBD Vertical angles are congruent.
ABE ≅
CDB AAS
AB ≅ CB
Corresponding Pts of
Congr
.
s are Congruent (CPCTC)
Slide14
GEOMETRY FINAL REVIEW-ch. 1
In the triangle below, how long is AC? 69.11014.1 B(7,5) A(-2,-3) C(7,-2)
BSlide15
GEOMETRY FINAL REVIEW-ch. 8
The hypotenuse of a 45°-45°-90° triangle measures 10 inches. What is the area of the triangle?A) 25 in2B) in2
C
)
50
in2 in2
ASlide16
GEOMETRY FINAL REVIEW-ch. 8
Triangle ABC is equilateral, with side lengths of 10 inches. What is the length, in inches, of AD?A)VB)
C) 5
D) 5
DSlide17
GEOMETRY FINAL REVIEW-ch. 8
What is the m< R, to the nearest degree, in the figure below?A) 60° B) 36°C)30°D) 27°
ASlide18
GEOMETRY FINAL REVIEW-ch. 8
At a distance of 20 m from a building, a person who is 3 m tall looks up at an angle of 25° to see the top of the building. How tall is the building to the nearest meter?(HINT: Draw a picture)A)8 mB) 9 mC) 12 m D)18 m
BSlide19
GEOMETRY FINAL REVIEW-ch. 8
Find the length of the hypotenuse, to the nearest tenth of a centimeter, of a right triangle if one angle measures 70° and the adjacent leg measures 8 cm. (HINT: Draw a picture)23.4 cm Slide20
GEOMETRY FINAL REVIEW-ch. 8
Find the value of a in the figure below, to the nearest whole number. A) 10B) 11 C) 14D) 16
BSlide21
GEOMETRY FINAL REVIEW-ch. 6
In the parallelogram below, WV = 5x + 2 and YV = -x + 20. Find WY.A) 17B) 20C) 34
D) 50
CSlide22
GEOMETRY FINAL REVIEW-ch.6
In the parallelogram below, m < ABC = 70°. Find m < ACD.m<ACD=65⁰Slide23
GEOMETRY FINAL REVIEW-ch.6
The perimeter of the figure below is 48. Find the value of x.X=7Slide24
1) AC and BD bisect each other.
1) Given2) 2) Definition of Bisect
BEC
DEA 3) _____________________ BEA DEC BEC
DEA 4) ________________
BEA DEC
1
2
5)__________________
3
4
6
)
6
) Alternate Interior Angles
Theorem
7)_______________ 7
) Definition of Parallelogram
Vertical angles are
.
SAS
CPCTC
(
Corr. Parts or congruent triangles
are
ABCD
is a parallelogram.
Complete the proof of the following statement:
If the diagonals of a quadrilateral bisect each
other
,
then
the quadrilateral is a parallelogram
.
Given
: AC and BD bisect each
other
.
Prove
:
ABCD
is a parallelogram
.
GEOMETRY FINAL REVIEW-
ch.
6
Converse ofSlide25
GEOMETRY FINAL REVIEW-ch. 11
A trapezoidal prism has ____ total faces.A) 4B) 5C) 6 D) 7A)4Slide26
GEOMETRY FINAL REVIEW-ch. 11
If a plane intersects a cube, the intersection of the plane and cube cannot be a(an) ___________.a) Triangleb) Squarec) Rectangled) Octagond) OctagonSlide27
GEOMETRY FINAL REVIEW-ch.1
AC starts at point A (1,4), and ends at point C (7, 13). What are the coordinates of the midpoint of AC? (4, 8.5)Slide28
GEOMETRY FINAL REVIEW-ch.1
Given points A (0, -3), B (5, 3), Q (-3, -1), which of the following points is a location of P so that PQ is parallel to AB?a) (0,3)b) (12,5)c) (-7,11)d) (2,5) dSlide29
GEOMETRY FINAL REVIEW-ch.12
Suppose triangle ABC has vertices A (-5,-2), B (-6,-2), and C (-6,-6). If triangle ABC is rotated 90° counterclockwise about the origin, what are the coordinates of the vertices of triangle A’B’C’? (HINT: use your reasoning skills)A’ (2,-5), B’ (2, -6), C’ (6, -6)A’ (-5,2), B’ (-6,2), C’ (-6,6)c) A’ (5,-2), B’ (6,-2), C’ (-6,-6)d) A
’ (2,-5), B’ (-2,-6), C’ (-6,-6)
aSlide30
GEOMETRY FINAL REVIEW-ch.12
How many lines of symmetry does the polygon shown have?a) 0b) 1 c) 2d) 31Slide31
GEOMETRY FINAL REVIEW-ch. 10
Find the area of the sector in circle P if PA = 10 cm and measure of arc APB = 36°.a) 10π cm2b) 20π cm2c) 36π
cm
2
d) 72π
cm2aSlide32
GEOMETRY FINAL REVIEW-ch. 10
Find the area of the shaded region.Area of square = 256 cm2 (16*16)
Area of circle = 64π cm
2
(82)Area shaded region = 256 - 64π cm
2 or
approx. 55.04 cm2Slide33
GEOMETRY FINAL REVIEW-
ch. 10In circle P, find the area of the shaded region. Use an approximate value of 3.14 for π.
a) 3.14
square units
b) 4.56
square unitsc) 6.28 square unitsd) 9.62 square unitsbSlide34
GEOMETRY FINAL REVIEW-ch. 10
In circle Q, find the measure of arc ADB. a) 42° b) 138°c) 222°
d) 318
cSlide35
GEOMETRY FINAL REVIEW-ch. 10
In circle P, find the length of arc AB if PA = 10 and m<APB = 36°. a) 2 π b) 0.556 π
c) 10
π
d) 12
πaSlide36
GEOMETRY FINAL REVIEW-ch.10
Apothem:
m
Area:
What is the length of the apothem of a regular hexagon with side length 8 m ? What is the area of the hexagon?Slide37
GEOMETRY FINAL REVIEW-ch. 10
The area of a sector of a circle is 54 π cm2. If the central angle is 60°, what is the radius of the circle? Radius = 18 cmSlide38
GEOMETRY FINAL REVIEW-ch. 11
Two cylinders have the same height. Their radii are 6 cm and 3 cm. What is the ratio of the volume of the cylinder with radius 6 cm to the volume of the cylinder with radius 3 cm? 4:1Slide39
GEOMETRY FINAL REVIEW-ch.11
If the volume of a cone is 96 π cm 3 and the base of the cone has a radius of 6 cm, find the height of the cone. 2.55 cm 8 cm16 cm48 cm
bSlide40
GEOMETRY FINAL REVIEW-ch. 11
Donna wants to put a ceramic castle whose volume is 350 cm3 and a plastic scuba diver whose volume is 250 cm3 in her aquarium as decoration. Her aquarium measures 40 cm X 30 cm X 30 cm high. The water is 2 cm from the top before she begins to decorate. How much will the water rise when she puts the castle and the diver in? 0.5 cm 1 cm
2 cm
6 cm
aSlide41
GEOMETRY FINAL REVIEW-ch. 11
Cube A has side lengths that are two times as long as the sides of cube B. How many times larger is cube A’s volume than that of cube B? 2468
dSlide42
GEOMETRY FINAL REVIEW-ch.
2 & ch. 6Consider these statements: Every square is a rhombus.Quadrilateral ABCD is not a rhombus. Which of these conclusions can be made using both statements?ABCD is not a parallelogram.
ABCD
is a rectangle.
ABCD
is not a square. ABCD is a trapezoidcSlide43
GEOMETRY FINAL REVIEW-ch. 2
Melanie, Nikki, and Donny are three students in a geometry class. Melanie is younger than Nikki, and Donny is older than Nikki.Which of these must be true? Donny is the youngest of the three students.Melanie is the youngest of the three students. Nikki is the oldest of the three students.
Melanie is the oldest of the three students.
bSlide44
GEOMETRY FINAL REVIEW-previous course
If the pattern shown below continues, how many squares will be in the next figure? 68
16
64
b
1 8 2 16 4 32Slide45
GEOMETRY FINAL REVIEW-ch. 2
The two statements below are true. All simkos are temas.All bollies are simkos. Using deductive reasoning, which of these statements must also be true?
All
temas
are
bollies.All simkos are bollies.All temas are simkos.All bollies are temas.
dSlide46
GEOMETRY FINAL REVIEW-ch. 5
Given: AF ≅ FC Use the word bank below the triangle to name each special segment in ΔABC. Word Bank: Median, Angle Bisector, Perpendicular Bisector, Altitude BF: ______________
FG
:
_______________
BF: MedianFG: Perpendicular BisectorSlide47
GEOMETRY FINAL REVIEW-ch. 5
Given: ABE ≅ EBC. Use the word bank below the triangle to name each special segment in ΔABC. Word Bank: Median, Angle Bisector, Perpendicular Bisector, Altitude BD: _____________
EB
:
______________ BD: AltitudeEB: Angle BisectorSlide48
GEOMETRY FINAL REVIEW-ch.3 and
ch. 4Jennifer has created a two-column proof as a response to the following question. Evaluate her argument to determine if you support or contradict her conclusion. Given: LA ≅PS, LS ≅PA Prove: LA ll PS
Statement
Reason
LA ≅ PS
1) GivenSL ≅ AP 2) GivenSA ≅AS 3) Same Segment/ReflexiveΔLAS ≅ΔPSA 4) SSSΔPSA ≅Δ LSA
5) Corresponding Parts of Congruent Triangles are Congruent
LA ll PS 6) Conv. Alt
.
Interior
angles
Thm
Determine if Jennifer’s argument is valid. Explain your reasoning. Support your answer with evidence from the diagram or Jennifer’s proof.
Jennifer’s argument is not valid. On step 5 of her proof, she states that
Δ
PSA
≅
Δ
LSA
. This would indicate that
LS
ll
PA and not LA
ll
PS. Jennifer should have stated that
Δ
LAS
≅
Δ
PSA
. Slide49
GEOMETRY FINAL REVIEW-
ch. 11BSlide50
GEOMETRY FINAL REVIEW-
ch. 1 and ch. 4
5. <ABD
6. SAS
Slide51
GEOMETRY FINAL REVIEW-ch. 1
Z(-6,1)Slide52
GEOMETRY FINAL REVIEW-ch.5
DSlide53
GEOMETRY FINAL REVIEW-ch.10
Calculate the area of the trapezoid. Area =