TEKS/STAAR - WCS - Homescihighgeometry.weebly.com/uploads/9/3/4/9/9349798/six_weeks_6.pdfâ TEKSING TOWARD STAAR Algebra I Geometry ® TEKS/STAAR SPIRALED PRACTICE 101 Geometry TEKSING

MATHEMATICS Geometry

TEKS/STAAR Spiraled Practice 101-120

Brenda DeBorde [email protected] Juanita Thompson [email protected]

TEKSING TOWARD STAAR ©2012

TEKSING TOWARD STAAR

Algebra I Geometry

®

TEKS/STAAR SPIRALED PRACTICE 101 Geometry

TEKSING TOWARD STAAR © 2012 1. Cat 1/G.3E 2. Cat 2/G.5B 3. Cat 4/G.8D Page 1

1. Given: a bP and c dP Prove : 1 2∠ ≅ ∠

We are given c dP . Therefore, we know 1 3∠ ≅ ∠ because corresponding angles of parallel lines intersected by a transversal are congruent. We are also given a bP . Therefore, we know 2 3∠ ≅ ∠ because alternate exterior angles of parallel lines intersected by a transversal are congruent. Thus

1 2∠ ≅ ∠ , because − A alternate exterior angles of parallel lines intersected by a transversal are congruent.

B corresponding angles of parallel lines intersected by a transversal are congruent.

C two angles congruent to the same angle will be congruent to each other.

D vertical angles are congruent. 2. The table below shows the number of distinct diagonals that can be drawn from one vertex of a

convex polygon.

Number of Sides

Polygon

Number of Diagonals

3

0

4

1

5

2

6

3

Based on the information in the table, how many distinct diagonals can be drawn from one vertex on a convex polygon with 9 sides?

F 7

G 5

H 6

J 8

a b

c

d

1

2 3 4



3. A can of mixed nuts is shown below. What is the surface area of the mixed nuts can? A 300π square centimeters

B 200π square centimeters

C 170π square centimeters

D 120π square centimeters

12 cm

10 cm

Mixed Nuts


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8B 2. Cat 5/G.11C 3. Cat 1/G.3C Page 1

1. »AB has a central angle of 45° . Circle P has a diameter of 24 centimeters.

What is the length of ¼ACB ? A 2π cm

B 6π cm

C 12π cm

D 3π cm

2. A right triangle is shown below.

Which of the following will be the lengths of the sides of a triangle similar to the one above? F 3, 4, 5

G 6, 8, 10

H 8, 15, 17

J 10, 24, 26

24 c

m

45° B

C

P

A

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8B 2. Cat 5/G.11C 3. Cat 1/G.3C Page 2

3. After observing several triangles, Joseph decided that the three altitudes of a triangle always

intersect in the interior of the triangle. Which triangle below can be used to contradict his decision?

A B C D


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5B 2. Cat 3/G.7B 3. Cat 4/G.8F Page 1

1. The volumes of three similar cones are given below. Cone 1: 10π cubic units Cone 2: 80π cubic units Cone 3: 640π cubic units Cone 4: ? Each cone in the pattern was enlarged by the same scale factor as the one before it. If the pattern

continues, what will be the volume of cone 4? A 1280π cubic units

B 2560π cubic units

C 5120π cubic units

D 10,240π cubic units

2. Which of the following lines will be parallel to the line with equation 3 2 2x y+ = ?

F 4 3 6x y+ = −

G 3 2 5x y− =

H 6 4 3x y+ = −

J 2 3 3x y− =

3. Ms. Longley needs 112 feet of fencing to enclose a pen for her animals. She bought a roll of fencing

that has 35 meters on it. If 1 foot is approximately 0.305 meter, which statement below best describes if she will have enough fencing?

A No, she will need about 0.84 meters more fencing.

B No, she will need about 2.4 meters more fencing.

C Yes, she will have less than 1 meter of the fencing left over.

D Yes, she will have exactly the right amount of fencing.



1. The sides of a quadrilateral are 5 inches, 6 inches, 9 inches and 8 inches. If a random point is

chosen from the sides of the quadrilateral, what is the probability it will be on the shortest side?

A 528

C 523

B 14

D 314

2. Given square ABCD below. E,F,G and H are the midpoints of the sides as shown.

Ann made the statement that quadrilateral EFGH is a rhombus. She justified her statement with the following argument: Since E,F,G and H are the midpoints of the sides of the square , FG DBP ,

0.5FG DB= , EH DBP and 0.5EH DB= and because in a triangle the segment that joins the midpoints of two sides of a triangle is parallel to the third side and measures half of it. Likewise, HG ACP , 0.5HG AC= , EF ACP and 0.5EF AC= . AC DB= because the diagonals of a square are equal in length. Thus FG EHP and EF HGP because two lines parallel to the same line will be parallel to each other. Also EH FG GH EF= = = because they are half of segments of the same length. Quadrilateral EFGH is a rhombus because −

F it has opposite sides parallel

G it has four sides

H it has right angles

J it has opposite sides parallel and is equilateral.

3. Identify which of the following are not Pythagorean triples? A a = 8, b = 15, c = 17

B a = 5, b = 12, c = 13

C a = 3, b = 4, c = 5

D a = 3, b = 9, c = 3 10

A

H

G

F

D C

B

E


TEKSING TOWARD STAAR © 2012 1. Cat 3/G.6A 2. Cat 4/G.8D 3. Cat 5/G.11D Page 1

1. A square pyramid is intersected by a plane 8 inches above base and parallel to the base of the

pyramid. The shaded region shows the intersection of the pyramid with the plane. The pyramid has a height of 18 inches and the base edges are 9 inches.

Which of the following best describes the intersection? A The intersection will be a square that has a side length of 6 inches.

B The intersection will be a square that has a side length of 5 inches.

C The intersection will be a square that has a side length of 4 inches.

D The intersection will be a square that has a side length of 4.5 inches.

2. A lunch pail is composed of a rectangular prism and half of cylinder. The diameter of the cylinder is 6 inches and the length of the cylinder is 11 inches. The base of the prism is a 6-inch square.

What is the approximate surface area of the lunch pail? F 350 square inches

G 707 square inches

H 430 square inches

J 416 square inches

9 inches

8 inches 18 inches



3. A rectangle is 12 inches wide and 14 inches long. The rectangle is enlarged by increasing the width by 3 inches and doubling the length. Which of the following statements best describes the perimeter of the new rectangle?

A The perimeter of the new rectangle will be 17 inches more than the old perimeter.

B The perimeter of the new rectangle will be 20 inches more than the old perimeter.

C The perimeter of the new rectangle will be 34 inches more than the old perimeter.

D The perimeter of the new rectangle will be 42 inches more than the old perimeter.


TEKSING TOWARD STAAR © 2012 1. Cat 1/G.2A 2. Cat 2/G.5B 3. Cat 4/G.9D Page 1

1. Given : AB

Brad was to locate point C on AB so that 12

ACCB

= . Which of the following constructions shows the

task accomplished?

2. A young child stacked his building blocks as shown below. He had only stacked the blocks four rows

high.

Each block has a volume of 1 cubic unit. If the stacking continues until it is 12 rows high, what will be the volume of the stacked blocks? F 60 cubic units H 156 cubic units

G 144 cubic units J 72 cubic units

A B

A B

A B

C

A B

C

C

A B C

A B

C D



3. A three-dimensional figure has 12 edges, 7 faces, and 7 vertices. Which of the following could be

the name of the figure?

A Pentagonal pyramid

B Hexagonal pyramid

C Pentagonal prism

D Hexagonal prism


TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11A 2. Cat 4/G.9C 3. Cat 1/G.1C Page 1

1. Quadrilateral ABCD is shown below.

Which quadrilateral below best represents a dilation of quadrilateral ABCD using a scale factor of 23

?

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

A

B

C

D

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

A

B

C

D x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

B ′

C ′

D ′

A ′

A ′

B ′

C ′

D ′

D ′

A ′ C ′

B ′

B ′

A ′ C ′

D ′


TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11A 2. Cat 4/G.9C 3. Cat 1/G.1C Page 2

2. CA and CB are tangent to circle E. The measure of ∠ ACB is 50 ° . What is the measure of ∠AEC ?

F °75

G °70

H °65

J °40

3. Which of the following geometries can have less than 180 ° in the sum of the measures of the angles of a triangle?

A Spherical

B Hyperbolic

C Euclidean

D Not Here

A

C D E

B


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5D 2. Cat 3/G.7C 3. Cat 4/G.8A Page 1

1. ∆DEF is a right triangle.

What is the length of FE ?

A 45 cm

B 15 cm

C 30 cm

D 30 3 cm

2. DEF∆ is shown on the grid below.

Which of the following best represents the perimeter of this triangle? F 47 units

G 28 units

H 53 units

J 137 units

°60

D

E

F

15 3 cm

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

D

E

F


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5D 2. Cat 3/G.7C 3. Cat 4/G.8A Page 2

3. What is the area of an equilateral triangle with a perimeter of 24 units?

A 64 square units

B 16 3 square units

C 32 3 square units

D 16 square units


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.9A 2. Cat 5/G.11C 3. Cat 2/G.5B Page 1

1. Three linear pair angles with their angle bisectors are shown below.

After observing the drawings, Ronald conjectured that the angle bisecting rays would be perpendicular to each other. Which of the following statements best supports his conjecture?

A The bisecting rays are perpendicular to the exterior rays of the linear pair and thus are

perpendicular to each other.

B The bisecting rays share an endpoint thus they intersect each other and therefore are perpendicular.

C The bisecting rays bisect one obtuse angle and one acute angle so they will form a right angle. Therefore, they are perpendicular.

D A linear pair of angles has measures that total 180 ° . The angle that is formed by the two bisecting rays is formed by one-half of each of the two original angles. Since one-half of 180 ° is 90 ° , the angle formed by the two rays is a right angle. Therefore, the angle bisecting rays are perpendicular to each other.

2. In right triangle ABC∆ , hypotenuse AB is 75 units and leg AC is 43 units. What is the measure of the

acute angles of the triangle to the nearest degree?

F ∠ = ° ∠ = °35 and 55 m A m B H ∠ = ° ∠ = °48 and 42 m A m B

G ∠ = ° ∠ = °55 and 35 m A m B J ∠ = ° ∠ = °60 and 30 m A m B

3. Given: Circle P and two intersecting chords. The segments created by the intersection have lengths

a, b, c and d as shown. The table shows some possible values for these lengths.

Which of the following statements will be true about the segments of the intersecting chords? A The sum of a and b will be more than the sum of c and d.

B The product of a and b will be more than the product of c and d.

C The product of a and b will be equal to the product of c and d.

D The product of a and c will be equal to the product of b and d.

P a

b c

d a b c d 4 3 2 6 12 4 6 8 9 4 6 6



1. The coordinates of the vertices of a quadrilateral are ( − 6, 1), ( − 4, 7), ( − 1, 8), and ( − 3, 2). The

best description of this quadrilateral is −

A a rectangle

B a parallelogram

C a square

D a trapezoid

2. A cone has height of 10 units and a radius of 6 units. A cylinder has height of 12 units and a radius of 6 units. Which is closest to the volume of the composite figure that is two congruent cones and a cylinder represented in the drawing?

F 1,733 cubic units

G 2,111 cubic units

H 339 cubic units

J 3,390 cubic units

10

12

6

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10



3. A triangle is dilated with a scale factor of 0.5 to create a similar triangle. If the area of the original

triangle is 72 square inches, what is the area of the new triangle, in square inches?

Record your answer and fill the bubbles. Be sure to use the correct place value.

0 0 0 0 0 0 0

1 1 1 1 1 1 1

2 2 2 2 2 2 2

3 3 3 3 3 3 3

4 4 4 4 4 4 4

5 5 5 5 5 5 5

6 6 6 6 6 6 6

7 7 7 7 7 7 7

8 8 8 8 8 8 8

9 9 9 9 9 9 9

+ -

. . . . . . .


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8D 2. Cat 2/G.5B 3. Cat 3/G.7C Page 1

1. A triangular prism has an equilateral triangle base whose sides are 6 meters in length. The height

of the prism is 3 meters.

Which is closest to the volume of the prism?

A 46.8 cubic meters

B 54.0 cubic meters

C 187.1 cubic meters

D 18.6 cubic meters

2. On the map below, Third Avenue and Fourth Avenue are parallel streets. A local garden club

proposed to build a flower garden and fountain on the triangular section of land formed by the intersections of the streets as shown.

What are the measures of the three angles of the proposed garden and fountain site? F ° ° °45 , 45 , 90

G ° ° °40 , 50 , 90

H ° ° °30 , 60 , 90

J ° ° °10 , 20 , 150

3 m

6 m

Proposed Flower Garden and Fountain Site

°150

Third Avenue Fourth Avenue

Main

Logan


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8D 2. Cat 2/G.5B 3. Cat 3/G.7C Page 2

3. The midpoint of AB is D. If the coordinates of D are ( −

11 , 52

) and the coordinates of B are

(4, − 2), what are the coordinates of A?

A ( − 1, − 8)

B ( − 2, − 9)

C ( −112

, − 8)

D ( − 2, − 7)


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8B 2. Cat 5/G.11B 3. Cat 1/G.3B Page 1

1. »AB has a central angle of 60° . The circle has a diameter of 24 centimeters.

What is the best estimate of the area of the sector bounded by »AB ?

A 100 cm 2 C 18 cm 2

B 75 cm 2 D 452 cm 2 2. Look at the diagram below. PRS VT . Determine the value of x. F 6 H 4

G 3 J 8

3. Which of the following statements is not true about all isosceles triangles?

A The base angles will be congruent.

B The legs will be congruent.

C The sum of the three angles will be 180 ° .

D The base will be longer than either leg.

24 c

m

°60 B

A

12 6

12

x R

T

S

U V


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5B 2. Cat 3/G.6A 3. Cat 4/G.8C Page 1

1. A square has the midpoints of its sides joined as shown below. The figure created is also a square.

If the midpoints of the sides of this square are joined to form a smaller square, what will be the ratio of the length of the sides of the original square to this smallest square?

A The ratio of the length of the side of the original square to the length of the side of smallest square is 2 : 1.

B The ratio of the length of the side of the original square to the length of the side of smallest square is 2 2 : 1.

C The ratio of the length of the side of the original square to the length of the side of smallest square is 2: 1.

D The ratio of the length of the side of the original square to the length of the side of smallest square is 3: 1.

2. A square pyramid has a plane intersecting it perpendicular to the base and passing through the

vertex of the pyramid and the center of the base. A side view of this intersection is shown below. Which of the following best describes the intersection?

Plane

Lateral edge of the pyramid

F G

H J


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5B 2. Cat 3/G.6A 3. Cat 4/G.8C Page 2

3. Mr. James left his house and drove 8 miles north and then 5 miles west to the store. Which of the

following best describes the procedure for finding the straight-line distance from his house to the store?

A Use c = 8 and a = 5 in the equation + =2 2 2a b c and solve for b

B Use c = 8 and a = 5 in the equation + =2 2 2a b c , solve for b and then find a + b + c

C Use b = 8 and a = 5 in the equation + =2 2 2a b c and solve for c

D Use b = 8 and a = 5 in the equation + =2 2 2a b c , solve for c and then find a + b + c


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8D 2. Cat 1/G.3C 3. Cat 2/G.5C Page 1

1. A sphere has a circumference of 18π units. What is the volume of the sphere? A 7,776π cubic units

B 108π cubic units

C 727π cubic units

D 972π cubic units

2. In ∆WXY , <WY YX and <YX WX . Which statement must be true?

F ∠ < ∠ < ∠m X m Y m W

G ∠ < ∠ < ∠m X m W m Y

H ∠ < ∠ < ∠m Y m X m W

J ∠ < ∠ < ∠m W m Y m X

3. Mary created a tessellation using the equilateral triangle shown below. Which transformations did Mary use to create her tessellation? A Translations only

B Translations and reflections

C Translations, reflections and rotations

D Translations and rotations

Circumference: 18π


TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7C 2. Cat 4/G.10A 3. Cat 5/G.11D Page 1

1. A rectangle has vertices F(3, 4), G(5, 6), H(9, 2) and J(7, 0). What is the slope of the diagonal GJ?

A 3

B − 3

C 2

D −13

2. Figure EFGH is shown on the coordinate plane below.

Which of the following creates an image with G′ at (4, − 1) and E′ at ( − 2, − 3)?

F Reflect across the x-axis.

G Rotate about the point (0, 0).

H Reflect across the line y = 1.

J Translate down 2 units.

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

E

H G

F


TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7C 2. Cat 4/G.10A 3. Cat 5/G.11D Page 2

3. A company uses two similar rectangular prisms to ship their product. The larger prism has

dimensions that are 2.5 times the dimensions of the smaller prism. Based on this information, which of the following statements is true?

A The volume of the larger prism is 2.5 times the volume of the smaller prism.

B The volume of the larger prism is 6.25 times the volume of the smaller prism.

C The volume of the larger prism is 7.5 times the volume of the smaller prism.

D The volume of the larger prism is 15.625 times the volume of the smaller prism.

2.5 z

2.5h

2.5w

z

h

w


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.10B 2. Cat 2/G.5D 3. Cat 3/G.7B Page 1

1. ∆ ∆ TSR and PQR are shown below. T, Q and R are collinear points.

∠ ≅ ∠TRS PRQ , and ≅TS PQ . Which additional condition is sufficient to prove ∠ ≅ ∠T P ?

A RS RQ≅ C PQ TR⊥

B TR PR≅ D S Q∠ ≅ ∠

2. Given a, b, and c are the sides of a right triangle and are Pythagorean triples. Which of the

following could be values for a, b, and c?

F a = 1, b = 1, c = 2 2 H a = 3, b = 4, c = 5

G a = 1, b = 2, c = 3 J a = 5, b = 10, c = 12

3. If the following pairs of lines were graphed in a coordinate system, which pair could describe the

bases of a trapezoid?

A + = + =3 5 8 and 5 3 6x y x y C + = + =2 3 2 and 3 2 12x y x y

B + = + =5 3 4 and 3 5 12x y x y D − = − = −2 3 8 and 4 6 3x y x y

a

b

c

R S

Q

P T


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8A 2. Cat 5/G.11C 3. Cat 1/G.2A Page 1

1. A circle has a circumference of 18π feet. What is the area of the circle?

A 18π square feet

B 36π square feet

C 81π square feet

D 27π square feet 2. Which equation can be used to solve for x?

F ° tan 49 = 12x

G ° 12tan 49 = x

H ° cos 49 = 12x

J ° 12sin 49 = x

3. Barney constructed the median to side BC in ABC∆ as shown below. Which of the following statements can be validated from the information in the construction?

A ABD ADC∆ ≅ ∆

B ABD ADC∠ ≅ ∠

C AD is a perpendicular bisector of BC .

D D is the midpoint of BC .

x

12

°49

A

B

C

D



1. Triangle CDE is an isosceles triangle. The measure of the vertex angle is x ° .

Which of the following expressions can be used to find the measure of ∠D ?

A − −180 x x C −1802x

B −1802

x D −2 180x

2. Which of the following lines cannot define the base and the altitude to the base of a triangle? F + = + = −4 and 5x y x y H + = − = −2 6 and 2 3x y x y

G − = + = −3 4 and 3 1x y x y J = + − = −2 6 and 2 4y x x y

3. A base of a cone has a radius of 6 inches. The altitude makes a 30 o with the slant height as shown

in the drawing.

The approximate volume of the cone to the nearest cubic inch will be − A 226 in.3 C 452 in.3

B 392 in.3 D 1,357 in.3

E D

C

x°

30 o

6 in.


TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11C 2. Cat 1/G.3E 3. Cat 4/G.8D Page 1

1. ∆RST is a right triangle with ⊥RQ ST . Which of the following statements is true?

A =RS RTSQ TQ

B =RS RTSQ RS

C =RQ RTRS RQ

D =ST RTRT QT

2. Which of the following statements about an isosceles trapezoid can not be justified? F The bases are parallel

G The legs are congruent.

H Each pair of base angles is congruent.

J The median is the geometric mean of the bases.

3. A cylinder has a height of 32 centimeters and a base area of 64π square centimeters. What is the

lateral surface area of the cylinder? A 2048π square centimeters

B 512π square centimeters

C 576π square centimeters

D 384π square centimeters

R

S T

Q


TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7C 2. Cat 4/G.9D 3. Cat 5/G.11D Page 1

1. A diameter of a circle has endpoints P (4, − 4) and Q ( − 11, 2). Which of the following best

represents the length of the radius of the circle?

A 6.3 units

B 8 units

C 16 units

D 22 units

2. A three-dimensional figure has 16 edges, 9 faces, and 9 vertices. Which of the following could be

the name of the figure? F Rectangular prism

G Hexagonal pyramid

H Hexagonal prism

J Octagonal pyramid

3. A rectangular prism has a volume of 80 cubic units. If all the dimensions are all changed to 1

2 of

their original size, what will be the volume of the new rectangular prism? A 40 cubic units

B 20 cubic units

C 10 cubic units

D 160 cubic units

Documents

TEKS/STAAR - WCS - Homescihighgeometry.weebly.com/uploads/9/3/4/9/9349798/six_weeks_6.pdfâ TEKSING TOWARD STAAR Algebra I Geometry ® TEKS/STAAR SPIRALED PRACTICE 101 Geometry TEKSING