Download Review Area 2D Right Triangles and Circles

The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account the time spent on the topic in this unit.
Sample problems are written to meet the rigor of the TEKS.
Unit: 2-D Figures
Topics
tested
Dimensional
Change
TEKS
Sample Test Questions
G.10B
The side length of a smaller square is one-third the side length of a larger square.
Which of the following statements describes the area of the smaller square?
F The area of the smaller square is
1
the area of the larger square.
27
G The area of the smaller square is
1
the area of the larger square.
6
H The area of the smaller square is
1
the area of the larger square.
9
J The area of the smaller square is
1
the area of the larger square.
3
The area of a figure quadrupled from 10 ft 2 to 40 ft2. What can be determined
about the perimeter after the transformation?
A The perimeter doubled.
B The perimeter stayed the same.
C The perimeter quadrupled.
*D There is not enough information to determine the change in perimeter.
Dalia drew the trapezoid JKLM.
Which of the following will allow Dalia to create a new trapezoid with half the area
of trapezoid JKLM?
I.
Draw a trapezoid in which each base is half as long as in trapezoid JKLM.
II. Draw a trapezoid in which the height is half as long as in trapezoid JKLM.
III. Draw a trapezoid in which every dimension is half the corresponding
dimension in trapezoid JKLM.
A I only
B II only
C III only
D I and II only
Composite
Area
G.9A
G.11A
G.11B
Find the approximate area of the heart figure below.
A 804 cm2
B 1245 cm2
C 1647 cm2
D 2049 cm2
Two regular hexagons with center C and apothems a and b are shown in the figure
below. Each vertex of the smaller hexagon is a midpoint on a side of the larger
hexagon.
If
a  12 3cm and b  18cm , what is the total area of the shaded regions?
A
648 3cm 2
B
36 3cm 2
C
216 3cm 2
D 1,512 3cm
2
A rock garden has the shape of a regular pentagon with side length 4 feet.
Surrounding the rock garden is a circular fence at a distance of 8 feet from each
vertex of the pentagon. Grass covers the area between the pentagon and the
circle. Find the area of the grass.
A 408.3 square feet
B 380.8 square feet
C 71.6 square feet
D 44.1 square feet
Points A, B, C, and D are the vertices of a square. Points E and F are congruent
semicircles that are tangent to each other at point G.
Which value is closest to the area of the shaded region?
A 7.7 units2
B 4.3 units2
C 17.2 units2
D 64.3 units2
Within a square section of land, a landscaper will build a path, as represented by
the shaded section in the diagram below.
What is the area of the path?
A 48.7 ft2
B 71.3 ft2
C 97.4 ft2
D 168.8 ft2
Area
Probability
G.13B
In the spinner modeled below, Sector 1 has twice the area of Sector 3.
If the arrow is spun once, what is the probability that the arrow will land in Sector
1?
1
3
1
B
4
A
1
6
2
D
3
C
The figure shows a composite figure formed by two right triangles, a square, and a
circle. Determine which statement is not the correct probability of throwing a dart
into each shape.
A The probability of landing in the circle is

8
.
B The probability of landing in one of the smaller
C The probability of landing in the square is
triangles is
1
.
4
1
.
2
TEKS
G.9A determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios
sine, cosine, and tangent to solve problems
G.10B determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface
area, or volume, including proportional and non-proportional dimensional change
G.11A apply the formula for the area of regular polygons to solve problems using appropriate units of measure
G.11B determine the area of composite two-dimensional figures comprised of a combination of triangles,
parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of
measure
G.13B determine probabilities based on area to solve contextual problems
Unit:
Topics tested
Special Right
Triangles
TEKS
G.9B
Sample Test Questions
Two vertical poles are connected by a cable, as shown.
What is the approximate distance between the two poles?
A 4.47 m
B 7.21 m
C 10 m
D 20 m
Carrie is creating a logo in the shape of an isosceles triangle whose legs measure
17 cm each and whose base is 16 cm. What is the length of the altitude from
the vertex to the base of the triangular logo?
A 5.7 cm
B 15 cm
C 18.8 cm
D 24 cm
The diameter of Circle T is 10 units.
What is the perimeter of RTU ?
A
10 3
B
15 2
C
10  5 2
D
10  5 3
The shape of a new park in Sugar Land is an equilateral triangle. The city wants
to construct a 50 food sidewalk from the midpoint of one side of the triangle to
the opposite vertex. What is the area of the park?
A 7500 feet
B
5000
3 feet
3
C 2500
D
3 feet
2500
3 feet
3
A circus acrobat uses a trampoline and two platforms for part of his act, as
shown.
The starting platform has a height of 5 feet. The height of the landing platform
can be found by doubling the height of the starting platform and then adding 2
feet. Approximately how far apart are the two platforms?
A 7 feet
B 9 feet
C 11 feet
D 12 feet
Trigonometry
G.9A
Find the approximate length of the diameter of Circle R.
A 11.48 in.
B 14.72 in.
C 24.45 in.
D 27.69 in.
A ship is at position A on the sea surface and locates a wreck on the seabed 315
meters directly below. The ship then moves 530 meters due west until it
reaches position B.
From its new position at B, what is the approximate angle of depression from the
ship to the wreck?
A
31
B
36
C
54
D
59
A dead tree was struck by lightning, causing it to fall over at a point on the
ground 15 feet from the base of the tree.
If the fallen tree top forms a
was the tree originally?
34 angle with the ground, approximately how tall
A 10 feet
B 18 feet
C 28 feet
D 31 feet
Nick and Owen are visiting the Egyptian Pyramids. From where Nick is standing,
the angle of elevation to the top of the pyramid is 52 . From Owen’s position,
the angle of elevation is 58 .
If they are standing 70 feet apart, and each of their eye level is 5 feet above the
ground, how tall is the pyramid?
A 144 ft
B 438 ft
C 506 ft
D 924 ft
The 2nd floor of the mall is 19 feet above the 1st floor.
What is the approximate angle of elevation created by the 30 foot escalator
from the 1st floor to the 2nd floor?
A
32
B
39
C
51
TEKS
G.9A determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios
sine, cosine, and tangent to solve problems
G.9B apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem,
including Pythagorean triples, to solve problems.
Unit: Circles and Proofs
Topics tested
TEKS
Sample Test Questions
Circles:
Proportional
Relationships
G.12B
G.12B
G.12C
The minute hand of a clock is 3 inches long. Which of the following is the
best estimate of the distance the tip of the hand moves as the time
changes from 12:30 to 12:45?
G.12D
A 0.8 in
B 2.4 in
*C 4.7 in
D 9.4 in
G.12B
Circle P as a radius of 10 inches.
If
mAB  22.7 inches, what is the measure of APB ?
A 26°
*B 130°
C 150°
D 260°
G.12C
Charis waters her lawn with a sprinkler that sprays water in a circular
pattern at a distance of 15 feet from the sprinkler. The sprinkler head
rotates through an angle of 300°, as shown by the shaded area in the
accompanying diagram.
What is the area of the lawn, to the nearest square foot, that receives
water from this sprinkler?
A
79 square feet
B
94 square feet
*C
D
589 square feet
707 square feet
G.12D
A dog has a 20 foot leash attached to the corner where a garage and a
fence meet, as shown in the accompanying diagram. When the dog pulls
the leash tight and walks from the fence to the garage, the arc the leash
makes is 15  feet.
What is the measure of the angle
radians?
A

2
3
4
*B
Equations in
Circles
C

D
4
3
G.2B
G.2B
G.12E
A graph of a circle is given.
 between the garage and the fence, in
What is the length of the diameter of the circle?
A
3
B
2 5
C
6
*D
4 5
G.12E
A circle with a center at (1,3) and radius of 4 is graphed below.
Which equation represents the circle after it has been translated right 4 and
down 2?
A
( x  1) 2  ( y  3) 2  4
B
( x  5) 2  ( y  1) 2  4
C
( x  1) 2  ( y  3) 2  16
*D
( x  5) 2  ( y  1) 2  16
G.12E
Which of the graphs represents a circle with the equation
( x  4) 2  ( y  2) 2  36 ?
Key Relationships
in Circles
G.5A
G.12A
*A
C
B
D
G.5A
Central angles and inscribed angles were constructed from the same arcs.
Based on the pattern provided, which statement is correct?
A Central angles are always half of inscribed angles with the same arc.
B Inscribed angles are always equal to central angles with the same arc.
C Inscribed angles are always twice the measure of central angles with the
same arc.
*D Central angles are always twice the measure of inscribed angles with
the same arc.
G.12A
In the diagram below,
NP is tangent to circle O . NP  24 and OP  25 .
What is the length of the diameter of circle O ?
*A
7
B
11
C
14
D
25
G.12A
In circle D ,
degrees.
BC is a diameter, DA is a radius, and mAB equals sixty
What is mCAD ?
*A
30°
B
50°
C
60°
D
70°
G.12A
The circle shown below has chords
measure of
XY is 130°, as shown.
What is the measure of
*A
Circle Proofs
G.12A
XY , XZ , and YZ , with XY  XZ . The
YXZ ?
50°
B
55°
C
60°
D
65°
Compete the following proof:
Given: BD and
Prove:
DB  DC
DC are tangent to Circle A.
Possible Solution:
Statement
1.
BD and DC are
Reason
1. Given
tangent to Circle A.
3. DBA and DCA
are right angles.
2. Tangent lines are
perpendicular to the
radius drawn to the
point of tangency.
3. Definition of
perpendicular
4. DBA and DCA
are right triangles.
4. Definition of right
triangle
2.
BA  BD, CA  CD
5.
BA  BC
6.
7.
DA  DA
DBA  DCA
8.
DB  DC
5. All radii of a circle
are congruent.
6. Reflexive Property
7. HL Theorem
8. C.P.C.T.C.
Given: TA and TB are tangent to Circle R.
In a written explanation, tell how you know the given statement and given
diagram cannot both be true.
TEKS
G.2B derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence
of segments and parallelism or perpendicularity of pairs of lines
G.5A investigate patterns to make conjectures about geometric relationships, including angles formed by parallel
lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of
quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a
variety of tools
G.12A apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to
solve non-contextual problems
G.12B apply the proportional relationship between the measure of an arc length of a circle and the circumference of the
circle to solve problems
G.12C apply the proportional relationship between the measure of the area of a sector of a circle and the area of the
circle to solve problems
G.12D describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the
radius of the circle
G.12E show that the equation of a circle with center at the origin and radius r is x 2  y 2  r 2 and determine the
equation for the graph of a circle with radius r and center (h,k), ( x  h)2  ( y  k )2  r 2 .