geometry- · 2020. 5. 31. · brownsville independent school district 1900 price road, brownsville,...

Geometry-B

Student Name: __________________

Student ID: _____________________

School Name: ___________________

Summer School Distance

Learning Packet

Teacher Name: __________________

High School Math

Brownsville Independent School District

1900 Price Road, Brownsville, TX 78521, (956) 548-8000 www.bisd.us

May 2020

Esteemed Parents and Family Members,

We hope this letter finds you safe and healthy amid this uneasy time of COVID-19. As always, our priority is

the safety and welfare of our students. Our 2020 summer program will continue by utilizing virtual learning

platforms and will begin on June 1 and end on June 18, 2020. The purpose of the summer program is to

provide students the opportunity to gain credit for the course your student has failed.

You have received this summer 2020 instructional packet for your (9th - 12th grade) student. This instructional

packet includes materials for the core area(s) your student has failed.

We ask that you contact your student’s school to:

• give you the failing subject area(s)

• give you your student’s summer teachers’ name and contact information / email address

• update any contact information including any changes and additional contact numbers, and

email addresses, etc.

• receive login information for the digital platform

The platform utilized this summer will be:

• 9th -12th Google Classroom

(Download Google Classroom app or access through the Clever Portal)

Our sincere hope is that your child will participate and take advantage of this opportunity for promotion that

will greatly support your child’s area(s) of educational need.

Please encourage your student to read, watch educational programs, and practice their writing and speaking

skills. This is also a great time to share family stories and traditions, play board games and enjoy family time.

As always, it is an honor to continue to serve you and we value your family's commitment in entrusting us with

your child's education.

BISD does not discriminate on the basis of race, color, national origin, gender, religion, age, or disability or genetic information in employment

or provision of services, programs, or activities.

Brownsville Independent School District

1900 Price Road, Brownsville, TX 78521, (956) 548-8000 www.bisd.us

Mayo de 2020

Estimados Padres y Miembros de Familia,

Esperamos que esta carta le encuentre a buen resguardo y en buena salud durante estos días difíciles del

COVID-19. Como siempre, nuestra prioridad es la seguridad y el bienestar de nuestros estudiantes. Nuestro

programa de verano 2020 continuará utilizando plataformas de aprendizaje virtuales y comenzará el 1 de junio

y terminará el 18 de junio de 2020. El propósito del programa de verano es proporcionar a los estudiantes que

no fueron promovidos al siguiente grado, una oportunidad para obtener la promoción.

Con el fin de trabajar en la promoción de su hijo/a al siguiente grado, usted ha recibido un paquete de

instrucción para el verano del 2020 para su hijo/a de preparatoria. Dicho paquete incluye materiales para la(s)

asignatura(s) que su hijo/a reprobó.

Le pedimos que se ponga en contacto con la escuela de su hijo/a para:

• darle el área(s) de materia(s) que está reprobando.

• darle el nombre del maestro/a de verano de su hijo/a y su correo electrónico

• actualizar cualquier información de contacto, incluyendo cualquier cambio y números

de contacto adicionales, y correo electrónico, etc.

• recibir la información para conectarse a las plataformas digitales

La siguiente plataforma virtual se utilizará este verano para la preparatoria:

• Google Classroom

(Descargar aplicación de Google Classroom o usar el portal de Clever)

Esperamos sinceramente que su hijo/a participe y aproveche esta oportunidad de promoción que apoyará en

gran medida las áreas de su necesidad educativa.

Anime a sus hijos/as a leer, ver programas educativos y practicar sus habilidades para escribir y hablar. Este es

también un gran momento para compartir historias y tradiciones familiares, jugar juegos de mesa y disfrutar

del tiempo en familia.

Como siempre, es un honor continuar sirviéndole y valoramos nuestro compromiso con su familia al

confiarnos la educación de su hijo/a.

BISD no discrimina de acuerdo de raza, color, origen nacional, género, religión, edad, información genética, o incapacidad en el empleo o en

la provisión de servicios, programas o actividades.

Geometry-B Summer 2020

Lesson TEK Description TEK Resources Pearson Realize

Week 1(June 1-June 5) T5L1 Midpoint and Distance in the

Coordinate Plane G.2B T5 Lesson 1

T6L1 The Polygon Angle-Sum Theorems G.5A T6 Lesson 1

T6L4 Properties of Rhombuses, Rectangles, and Squares G.5A T6 Lesson 4

Week 2 (June 7-June 12) T6L6 Trapezoids and Kites G.5A T6 Lesson 6

T9L1 Similar Polygons G.7B T9 Lesson 1

T10L1 The Pythagorean theorem and its Converse G.9B T10 Lesson 1

Week 3 (June 15-June 18) T10L2 Special Right Triangles G.9B T10 Lesson 2

T10L3 Trigonometry G.9A T10 Lesson 3

Finalize all assignments

Geometry-B

Student Name: __________________

Student ID: _____________________

School Name: ___________________

Summer School 2020

Week 1

Teacher Name: __________________

High School Math

Name Class Date

5-1 Practice Form G

Find the coordinate of the midpoint of the segment with the given endpoints.

1. 3 and 5 2. −7 and 4 3. 5 and −9 4. −6 and −10

Find the coordinates of the midpoint of AB .

5. A(6, 7), B(4, 3) 6. A(−1, 5), B(2, −3)

7. A(14, −2), B(7, −8) 8. A(0, 0), B(−5, 12)

9. A(2.8, 1.1), B(−3.4, 5.7) 10. 1 1 1(2 , ), (3 , 1)2 4 4

A B− −

The endpoints of are J(–3, –7) and K(5, 9). What are the coordinates of the following points on ?

11. point W is (1/4) the distance from J to K.

12. point R is (3/4) the distance from J to K.

13. point P is (1/8) the distance from J to K.

Find the distance between each pair of points. If necessary, round to the nearest tenth.

14. A(6, 7), B(−1, 7) 15. C(5, −5), D(5, 3)

16. E(−1, 0), F(12, 0) 17. Q(2, −6), T(10, 0)

18. H(20, −4), I(−4, 3) 19. J(−5, 5), K(−3, −2)

The room shown below right is 14 ft by 10 ft. Find the dimensions of each piece of furniture to the nearest tenth.

20. length and width of the dresser

21. length and width of the table

22. length and width of the bed

23. Reasoning The midpoint of AB is on the y-axis, and

AB is parallel to the x-axis. Point A is located in Quadrant

III. Which quadrant contains point B? Explain.

Midpoint and Distance in the Coordinate Plane

Name Class Date

5-1 Practice (continued) Form G

For each graph, find (a) X Y to the nearest tenth and (b) the coordinates of the midpoint of XY .

24. 25.

26. Coordinate Geometry Graph the points A(0, 0), B(3, 3), C(9, 3), and D(12, 0). Draw trapezoid ABCD and diagonals AC and BD . Add point E(6, 2) at the intersection of diagonals AC and BD . a. Find BE and CE. What do you notice? b. Find AE and DE. What do you notice? c. Make a Conjecture What appears to be true about the diagonals of a

trapezoid?

27. Open-Ended Point B(−3, −3) is the endpoint of many segments.

a. You know that a segment with endpoint B lies entirely in Quadrant III. What does that tell you about the other endpoint?

b. How many possible segments parallel to either the y-axis or the x-axis match this description? Explain.

28. The plan at the right shows three storage closets in an apartment building. Find the center of each closet and the length of the closet’s diagonal to the nearest tenth of a foot. (Hint: The diagonals bisect each other, so the center is the midpoint of each diagonal.) a. closet 1 b. closet 2

c. closet 3

29. A(x1, y1) and B(x2, y2) are the endpoints of the hypotenuse of a right triangle. Write a formula to find the distance between A and B.

Pearson Texas Geometry Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

Midpoint and Distance in the Coordinate Plane

Name Class

Date

6-1 Practice Form G

1. 2. 3.

4. 12-gon 5. 18-gon 6. 25-gon

7. 60-gon 8. 102-gon 9. 17-gon

10. 36-gon 11. 90-gon 12. 11-gon

Find the measure of one angle in each regular polygon. Round to the nearest tenth if necessary.

13. 14. 15.

16. regular 15-gon 17. regular 11-gon 18. regular 13-gon



Algebra Find the missing angle measures.

25. 26.

27. 28. 29.


The Polygon Angle-Sum Theorems

Find the sum of the angle measures of each polygon.

Name

Class

Date


30. 31. 32.

33. 34. 35.

Find the measure of an exterior angle of each regular polygon. Round to the nearest tenth if necessary.

36. decagon 37. 16-gon 38. hexagon

39. 20-gon 40. 72-gon 41. square

42. 15-gon 43. 25-gon 44. 80-gon

Find the values of the variables for each regular polygon. Round to the nearest tenth if necessary.

45. 46. 47.

48. Reasoning Can a quadrilateral have no obtuse angles? Explain.

The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle. Then find the number of sides.

49. 12 50. 6 51. 45

52. 40 53. 24 54. 18

55. 9 56. 14.4 57. 7.2

The Polygon Angle-Sum Theorems

Algebra Find the missing angle measures.

Name Class

Date

6-4 Practice Form G

Decide whether the parallelogram is a rhombus, a rectangle, or a

square. Explain. 1. 2. 3. 4. 5.

Find the measures of the numbered angles in each rhombus.

6. 7.

8. 9.

10. 11.

12. 13.

Algebra HIJK is a rectangle. Find the value of x and the length of each diagonal.

14. HJ = x and IK = 2x −7 15. HJ = 3x + 5 and IK = 5x −9

16. HJ = 3x + 7 and IK = 6x − 11 17. HJ = 19 + 2x and IK = 3x + 22

Properties of Rhombuses, Rectangles, and Squares

Name Class

Date


Algebra HIJK is a rectangle. Find the value of x and the length of each diagonal.

18. HJ = 4x and IK = 7x − 12 19. HJ = x +40 and IK = 5x

Determine the most precise name for each quadrilateral. 20. 21.

21. 23.

Algebra Find the values of the variables. Then find the side lengths.

24. square WXYZ 25. rhombus ABCD

28. Solve using a paragraph proof.

Given: Rectangle DVEO with diagonals DE and OV

Prove: ∆OVE ≅ ∆DEV


Properties of Rhombuses, Rectangles, and Squares

26. rectangle QRST 27. square LMNO

Geometry-B

Student Name: __________________

Student ID: _____________________

School Name: ___________________

Summer School 2020

Week 2

Teacher Name: __________________

High School Math

Name Class

Date

6-6

Find the measures of the numbered angles in each isosceles trapezoid.

1. 2. 3.

4. 5.

6. 7.

Algebra Find the value(s) of the variable(s) in each isosceles trapezoid.

8. 9. 10.

11. 12. 13.

Algebra Find the lengths of the segments with variable expressions.

14. 15. 16.


Trapezoids and Kites

Find XY in each trapezoid.

Form G Practice

Name Class Date

6-6

Practice (continued) Form G

17. CD is the midsegment of trapezoid WXYZ.

a. What is the value of x?

b. What is XY?

c. What is WZ?

18. Reasoning The diagonals of a quadrilateral form two acute and two obtuse angles at their intersection. Is this quadrilateral a kite? Explain.

19. Reasoning The diagonals of a quadrilateral form right angles and its side lengths are 4, 4, 6, and 6. Could this quadrilateral be a kite? Explain.

Find the measures of the numbered angles in each kite. 20. 21. 22. 23. 24. 25.

Algebra Find the value(s) of the variable(s) in each kite.

26. 27. 28.

For which value of x is each figure a Kite?

29. 30.


Trapezoids and Kites

Name Class Date

9-1 Practice Form G

List the pairs of congruent angles and the extended proportion that relates the corresponding sides for the similar polygons.

1. ABCD ~ WXYZ

2. ∆MNO ~ ∆RST

3. NPOM ~ TQRS

Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.

4. 5.

6.

Determine whether the polygons are similar.

7. an equilateral triangle with side length 6 and an equilateral triangle with side length 15

9. a triangle with side lengths 3 cm, 4 cm, and 5 cm, and a triangle with side lengths 18 cm, 19 cm, and 20 cm

8. a square with side length 4 and a rectangle with width 8 and length 8.5

10. a rhombus with side lengths 8 and consecutive angles 50º and 130 º, and a rhombus with side lengths 13 and consecutive angles 50 º and 130 º

Pearson Texas Geometry | Lesson 9-1 | Practice Form G Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

Similar Polygons

Name Class Date

9-1


11. An architect is making a scale drawing of a building. She uses the scale 1 in. = 15 ft. a. If the building is 48 ft tall, how tall should the scale drawing be? b. If the building is 90 ft wide, how wide should the scale drawing be?

12. A scale drawing of a building was made using the scale 15 cm = 120 ft. If the scale drawing is 45 cm tall, how tall is the actual building?

Determine whether each statement is always, sometimes, or never true.

13. Two squares are similar.

14. Two hexagons are similar.

15. Two similar triangles are congruent.

16. A rhombus and a pentagon are similar.

Find the value of y. Give the scale factor of the polygons.

17. ABCD ~ TSVU

18. The scale factor of RSTU to VWXY is 14 : 3. What is the scale factor of VWXY to

RSTU?

In the diagram below, ∆PRQ ~ ∆DEF. Find each of the following.

19. the scale factor of ∆PRQ to ∆DEF

20. m∠D

21. m∠R

22. m∠P

23. DE

24. FE

25. Explain why all isosceles right triangles are similar, but not all scalene right triangles are similar.

Pearson Texas Geometry | Lesson 9-1 | Practice Form G Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

Similar Polygons

Name Class Date

Practice Form G

The Pythagorean Theorem and Its Converse Algebra Find the value of y. Express in simplest radical form. The lengths of the sides of a triangle are given. Classify each triangle as acute, right, or obtuse.

7. 3, 8, 10 8. 4, 5, 7 9. 12, 15, 19

10. 10, 24, 26 11. 20, 21, 28 12. 20, 48, 52

13. A square has side length 10 yd. What is the length of a diagonal of the square? Express in simplest radical form.

14. A square has diagonal length 9 m. What is the side length of the square, to the nearest centimeter?

15. A repairman leans the top of an 8-ft ladder against the top of a stone wall. The base of the ladder is 5.5 ft from the wall. About how tall is the wall? Round to the nearest tenth of a foot.

16. Writing When field archeologists plan an excavation, or digging site, they place a rectangular grid over the surface to be dug up. An archeologist decides that the dimensions of such a grid will be 11 m by 15 m. She will place stakes at the corners of the grid. How can she make sure that she places the stakes in the correct location? Explain.

17. Write a different proof of the Pythagorean Theorem by calculating

the area of the square shown in two ways.

Pearson Texas Geometry

Corner 1 Corner 2

Corner 3 Corner 4

1. 2. 3.

4. 5. 6.

10-1

Name Class Date


The Pythagorean Theorem and Its Converse

For each pair of numbers, find a third whole number such that the three numbers form a Pythagorean triple.

18. 13, 84 19. 16, 12 20. 32, 60

21. 80, 18 22. 99, 20 23. 75, 100

Is each triangle a right triangle? Explain.

28. A square is drawn inside a circle so that its vertices touch the circle. If the radius of the circle is 15 cm, what is the perimeter of the square?

29. The playing surface of a football field is 300 ft long and 160 ft wide. If a player runs from one corner of the field to the opposite corner, how many feet does he run?

30. A line of roses forms the diagonal of a rectangular flower garden. The line of roses is 18.4 m long, and one side of the garden is 13 m long. To the nearest tenth of a meter, what is the length of a perpendicular side of the garden?

31. ΔABC has vertices A(4, –1), B(5 6), C(1, 3). Verify that without using the Slope Formula.

32. ΔEFG is an obtuse triangle. Two of its sides measure 13 cm and 7 cm. What is the range of possible values for its third side to the nearest tenth of a centimeter?

33. The International Space Station orbits 350 km above Earth’s surface. Earth’s radius is about 6370 km. Use the Pythagorean Theorem to find the distance from the space station to Earth’s horizon. Round your answer to the nearest 10 kilometers. (Diagram is not to scale.)


10-1

24.

26.

25.

27.

Geometry-B

Student Name: __________________

Student ID: _____________________

School Name: ___________________

Summer School 2020

Week 3

Teacher Name: __________________

High School Math

Name Class Date

Practice Form G

Special Right Triangles

Find the value of each variable. If your answer is not an integer, express it in simplest radical form. The side lengths of a triangle are given. Determine if the triangle is a 45°-45°-90° triangle, a 30°-60°-90° triangle, or neither.

7. 40, 50, 80 8. 31,31 2,62

9. 6 2,6 2,12 10. 11,11 3, 22

11. A square has side length 95. What is the length of the diagonal of the square? Express your answer in simplest radical form.

12. A square has diagonal length 13 m. What is the side length of the square, to the nearest centimeter?

13. A professional baseball diamond is a square. The distance from base to base is 90 ft. To the nearest foot, how far does a catcher standing at home plate throw the ball across the diagonal of the square to second base?

14. Children climb 8 ft to get to the top of a slide. The end of the slide is 1 ft above the ground and the slide rises at a 45° angle. If the slide makes a straight line from the top to the bottom, how far does a child travel down the slide? Round to the nearest foot.


1. 2.

3. 4.

5. 6.

10-2

Name Class Date


Special Right Triangles

15. You set up a makeshift greenhouse by leaning a square pane of glass against a building. The glass is 4.5 ft long, and it makes a 30° angle with the ground. How much horizontal distance between the building and the glass is there to grow plants? Round to the nearest inch.

16. A square tablecloth has a line of embroidered flowers along the diagonal. The tablecloth is 48 in. on each side. How long is the embroidery line? Round to the nearest inch.

17. An equilateral triangle has height 26 cm. What is the length of each side of the triangle, to the nearest centimeter?

Find the value of each variable. If your answer is not an integer, express it in simplest radical form.

22. Right triangle ABC has area 32 23 cm .The measure of A∠ = 30, Bm∠ = 90. What is the length of BC? AB? AC? Express all answers in

simplest radical form.

23. An equilateral triangle has perimeter 120 in. What is the area of the triangle? Express your answer in simplest radical form.

24. Open-Ended Write a real-life problem that you can solve using a 45°-45°-90° triangle with an 18-ft hypotenuse. Show your solution.


18. 19.

20. 21.

10-2

Name Class Date

Practice Form G Trigonometry

Write the ratios for sin X, cos X, and tan X.

Find the value of x. Round to the nearest tenth.

8. An escalator at a shopping center is 200 ft 9 in. long, and rises at an angle of 15°. What is the vertical rise of the escalator? Round to the nearest inch.

9. A 12-ft-long ladder is leaning against a wall. It reaches 11 ft 8 in. up the wall. What angle does the ladder make with the ground? Round to the nearest degree.

10. A school installs a ramp that will rest on a landing 3 ft high. According to building code, the ramp must make a 7º angle with the ground. To the nearest tenth of a foot, what should be the length of the ramp?

Find the value of x. Round to the nearest degree.


1. 2. 3.

4. 5.

6. 7.

11. 12.

13. 14.

10-3

Name Class Date

Practice (continued) Form G Trigonometry

15. The lengths of the diagonals of a rhombus are 4 in. and 7 in. Find the measures of the angles of the rhombus to the nearest degree.

16. The lengths of the diagonals of a rhombus are 5 in. and 8 in. Find the measures of the angles of the rhombus to the nearest degree.

Find the values of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree. 19. Writing Explain why tan 45° = 1. The sine, cosine, and tangent ratios each have a reciprocal ratio. The reciprocal ratios are cosecant (csc), secant (sec), and cotangent (cot). Use ∆ DEF and the definitions below to write each ratio.

20. csc D 21. sec D 22. cot D

23. csc F 24. sec F 25. cot F

26. An identity is an equation that is true for all the allowed values of the variable. Use what you know about trigonometric ratios to show that the equation

27. Reasoning Does sin A + sin B = sin (A + B) when 0 < A + B < 90?

Explain your reasoning.

28. A right triangle has a hypotenuse of length 10 and one leg of length 7. Find the length of the other leg and the measures of the acute angles in the triangle. Round your answers to the nearest tenth

29. A right triangle has an angle that measures 28. The leg opposite the 28° angle measures 13. Find the length of the other leg and the hypotenuse. Round your answers to the nearest tenth.


17. 18.

10-3

geometry- · 2020. 5. 31. · brownsville independent school district 1900 price road, brownsville,...

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