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10 Chapter School-Home Letter congruent Two figures that have the same size and shape. trapezoid A quadrilateral with only 1 pair of parallel sides. Dear Family, Throughout the next few weeks, our math class will be studying 2-dimensional and 3-dimensional figures. The students will use definitions to identify and describe characteristics of these figures. polyhedron A three-dimensional solid figure with flat faces that are polygons. lateral faces Polygon faces on a polyhedron that connect the bases. You can expect to see homework that includes identifying types of triangles and quadrilaterals. Here is a sample of how your child will be taught to classify a triangle by its sides. Classify a Triangle by its Sides A triangle has side lengths 3 in., 2 in., and 3 in. What type of triangle is it? STEP 1 STEP 2 Identify how many sides are equal. Determine the correct classification. two There are __ sides with equal lengths of A triangle with two equal sides is 3 in. isosceles ____. __. Tips Congruent Figures *`e% )`e% *`e% Congruent figures are figures that are the same. Corresponding sides and angles are equivalent. To make sure two figures are congruent, make a list of all the matching sides and angles and then verify that the measures for each pair are equal. © Houghton Mifflin Harcourt Activity Try to have students commit most of the classifications of triangles, quadrilaterals, and polyhedrons to memory. You can make a series of flash cards with the classifications on one side of the card and definitions and/or sketches of examples on the other side of the card. Chapter 10 P239 10 Capítulo Carta congruentes Dos figuras que tienen el mismo tamaño y la misma forma. para la casa trapecio Un cuadrilátero con solo 1 par de lados paralelos. Querida familia, Durante las próximas semanas, en la clase de matemáticas estudiaremos las figuras bidimensionales y tridimensionales. Usaremos las definiciones para identificar y describir las características de esas figuras. poliedro Un cuerpo geométrico tridimensional con caras planas que son polígonos. caras laterales Las caras poligonales de un poliedro que conectan las bases. Llevaré a la casa tareas con actividades para identificar diferentes tipos de triángulos y cuadriláteros. Este es un ejemplo de la manera como aprenderemos a clasificar un triángulo por sus lados. Clasificar un triángulo por sus lados Pistas Los lados de un triángulo miden 3 pulg., 2 pulg. y 3 pulg. ¿Qué tipo de triángulo es? PASO 1 PASO 2 Identifica cuántos lados son iguales. Determina la clasificación correcta. dos Hay __ lados que tienen la misma longitud 3 pulg. de ____. Figuras congruentes *glc^% )glc^% Un triángulo con dos lados iguales es *glc^% isósceles ____. Las figuras congruentes son figuras que son iguales. Los lados y los ángulos correspondientes son equivalentes. Para estar seguro de que dos figuras son congruentes, haz una lista de todos los lados y ángulos que corresponden uno con el otro y luego verifica que las medidas de cada par sean iguales. Anime a los estudiantes a memorizar las clasificaciones de los triángulos, los cuadriláteros y los poliedros. Puede hacer tarjetas nemotécnicas con las clasificaciones en un lado y las definiciones y/o ejemplos visuales en el otro lado de cada tarjeta. P240 © Houghton Mifflin Harcourt Actividad Lesson 1 Name MA.5.G.5.3 Solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurement. Estimate and Measure Angles Estimate the measure of each angle. Then use a protractor to find the measure. 1. / ASN 2. / NSG 30º Estimate: __ 25º Measure: __ Estimate: __ > Measure: __ 3. / GSE E C 4. / LSE 8 Estimate: __ Estimate: __ Measure: __ Measure: __ J < Find the measure of /A in each figure. 5. I K 8 J 6. 8 P 7. 8 : Q ; ____ © Houghton Mifflin Harcourt 8. Brad used a ____ 60° angle iron to reinforce the edge of a fence. Make a sketch of the angle iron using your protractor. 9 ____ 9. Two sides of Meredith’s property meet at a 110° angle. Make a sketch of their intersection using your protractor. Chapter 10 P241 Lesson Check (MA.5.G.5.3) 1. What is the measure of / T ? A 25º C 115º B 65º D 155º V 2. What is the measure of / U ? F 25º H G 40º I 155º Review Grade 5 75º T U (MA.5.G.5.3) 3. If you use a ruler to make line segment TU in the drawing above longer and name the point that is left of T, W, what is the measure of / VUW in your new drawing? 4. What is the measure of / V in the drawing above? A 140º F 15º B 130º G 75º C 50º H 105º D 40º I 165º (MA.4.G.5.1) 5. What is the best estimate for the measure of the angle below? 6. What is the best estimate for the measure of the angle below? A 45º F 45º B 90º G 90º C 120º H 120º D 180º I 180º P242 © Houghton Mifflin Harcourt Look Back Lesson 2 Name MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra) including the number of edges, faces, vertices, and types of faces. Compare Two-Dimensional Figures Write whether the two figures are congruent or not congruent. 1. 2. * 0' 0' (++ , *- (' * 0' 0' (++ , *- (' All corresponding sides and angles are equal. congruent ______ So, the figures are ___ . 3. 4. ______ 5. ______ 6. (', ., ., ('' (', /' © Houghton Mifflin Harcourt /' ('' ______ ______ 7. Triangles ABC and XYZ are congruent. / A is 8. Rectangles A and B are congruent. The base one half the size of / B. / Y is 90°. / C and / Z are both 45°. What is the measure of / A? of Rectangle A is 5 inches more than its height. The height of Rectangle B is 12 inches. What is the base of Rectangle A? ______ ______ Chapter 10 P243 Lesson Check (MA.5.G.3.1) 1. Which of the following is congruent to the 2. Which of the following is not congruent to the square below? triangle below? *]k *]k C A 3 ft 3 ft F H G I 3 ft 3 ft 3 ft D B 3 ft 3 ft 3 ft 3 ft Review Grade 5 (MA.5.G.5.2) 3. How many fluid ounces are in 4 cups of milk? 2 hour and 28 minute movie starts at 7:50 P.M. At what time will the movie end? 4. A A 20 fluid ounces F 9:18 P.M. B 32 fluid ounces G 9:78 P.M. C 40 fluid ounces H 10:08 P.M. D 64 fluid ounces I 10:18 P.M. (MA.4.G.5.1) 5. Which of the following angle measures is an acute angle? 6. Which of the following angle measures is an obtuse angle? A 33º F 47º B 90º G 60º C 100º H 90º D 107º I 123º P244 © Houghton Mifflin Harcourt Look Back PROBLEM SOLVING Name Act It Out Congruence • Lesson 3 MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Solve each problem. 1. Marcel has a quadrilateral that he thinks has two pairs of opposite congruent sides and four congruent angles, but he does not have any tools to verify. How can he check if the sides and angles are congruent? He can fold the ______ quadrilateral in half both ______ ways. If both sets of sides ______ and all angles line up, ______ then they are congruent. ______ 2. If the sides and angles do match up, what type of quadrilateral does Marcel have? 3. Richelle has a pentagon that she thinks has two pairs of congruent angles and two pairs of congruent sides. How can she check this without using any tools? ______ ______ ______ ______ ______ 4. Make your own sketch of what Richelle’s pentagon might look like. 5. Jerome has a triangle that he thinks has no equal © Houghton Mifflin Harcourt sides nor angles with the same measure. Without using a tool, how can he check? ______ ______ ______ 6. If the sides and angles are not equal, what type of triangle does Jerome have? ______ Chapter 10 P245 Lesson Check (MA.5.G.3.1) 1. A triangle has two equal sides and a third side that is five inches more than the length of the other two sides. If the perimeter of the triangle is 32 inches, what is the length of the longest side? 2. Triangle ABC is congruent to triangle DEF. AB is 3 cm, BC is 4 cm long, and CA is 5 cm long. Which of the following statements is not true? A 5 inches F FD is 12 cm long. B 9 inches G EF is 4 cm long. C 14 inches H FD is 5 cm long. D 16 inches I DE is 3 cm long. Review Grade 5 (MA.5.G.5.2) 3. How many ounces are in 50 pounds? 4. How many minutes are there in A 800 ounces F 4,000 minutes B 500 ounces G 2,400 minutes C 400 ounces H 960 minutes D 200 ounces I 240 minutes (MA.4.G.5.1) 5. Which of the following angle measures is NOT an acute angle? 6. Which of the following angle measures is a right angle? A 33º F 45º B 78º G 60º C 81º H 90º D 92º I 100º P246 © Houghton Mifflin Harcourt Look Back 40 hours? Lesson 4 Name MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Polygons Name each polygon. Then tell if it is regular or not regular. Make measurements if you need to. 1. 2. 4 sides, 4 vertices, 4 angles means it is a quadrilateral ___. The sides are regular not all equal, so it is not ___. 3. ______ 4. ______ 5. 6. ______ 7. Sketch nine points. Then, connect the points © Houghton Mifflin Harcourt ______ ______ 8. Sketch seven points. Then, connect the points to draw a closed plane figure. What kind of polygon did you draw? to draw a closed plane figure. What kind of polygon did you draw? ______ ______ Chapter 10 P247 Lesson Check (MA.5.G.3.1) 1. Which of the following is a regular pentagon? 2. Which of the following is NOT a regular polygon? A C F H B D G I Review Grade 5 (MA.5.G.5.2) 3. How much time elapses from 2:00 P.M.? 6:30 A.M. to 4. How many centimeters are there in one kilometer? A 5 hours 30 minutes F 100,000 centimeters B 6 hours G 10,000 centimeters C 7 hours 30 minutes H 1,000 centimeters D 8 hours I 100 centimeters (MA.4.G.6.2, MA.3.G.3.1) 5. Jenna is organizing her barrettes into boxes. 6. What polygon has She puts the same number of barrettes in each box. If there are 6 boxes and she has 30 barrettes, how many are in each box? G octagon A 35 H nonagon B 25 I decagon C 6 D 5 P248 10 sides? F heptagon © Houghton Mifflin Harcourt Look Back Lesson 5 Name MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Triangles Classify each triangle. Write isosceles, scalene, or equilateral. Then write right, acute, or obtuse. 1. 2. /dd -dd ),`e% ),`e% ('dd +)`e% None of the side measures are equal. So, it is scalene __ . There is a right right ___ angle, so it is a __ triangle. 3. 4. ,'Zd ___ ),`e% .`e% (,Zd )+`e% ,'Zd ___ ___ ___ ___ Measure and label the length of the sides in millimeters and the angles. Then, classify each triangle by the length of its sides and by the measure of its angles. 5. 6. © Houghton Mifflin Harcourt ___ ___ 7. Mary says the pen for her horse is an acute ___ ___ 8. Karen says every equilateral triangle is acute. right triangle. Is this possible? Explain. Is this true? Explain. ______ ______ Chapter 10 P249 Lesson Check (MA.5.G.3.1) 1. Which of the following triangles is impossible 2. What is the classification of the following triangle? to draw? A right obtuse triangle B right scalene triangle C acute isosceles triangle D obtuse scalene triangle Review Grade 5 F scalene H isosceles G right I acute (MA.5.G.5.3) 3. How many tons are in 40,000 pounds? 4. Which measurement is more precise? A 2 tons F 0.3 meter B 4 tons G 3 decimeters C 20 tons H 32 centimeters D 40 tons I 324 millimeters Look Back (MA.3.G.3.1) 5. How many sides does a hexagon have? 6. If a polygon has 8 sides, how many angles A 3 F 2 B 4 G 4 C 5 H 8 D 6 I 16 P250 © Houghton Mifflin Harcourt does it have? Lesson 6 Name MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Quadrilaterals Classify each quadrilateral in as many ways as possible. Write quadrilateral, parallelogram, rectangle, rhombus, square, or trapezoid. 1. 2. __ . It has 4 sides, so it is a quadrilateral None of the sides are parallel, so there is no other classification. . ____ 3. ______ 4. ______ 5. 6. ______ 7. Kevin claims he can draw a trapezoid with © Houghton Mifflin Harcourt ______ ______ 8. “A square is a regular quadrilateral.” Explain three right angles. Is this possible? Explain. whether this is true or false. ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ Chapter 10 P251 Lesson Check (MA.5.G.3.1) 1. A parallelogram has two pairs of parallel sides. Which classification can it NOT be? 2. Which of the following is NOT always true about a rhombus? A quadrilateral F All sides are equal. B rectangle G All angles are equal. C square H There are 2 pairs of parallel sides. D trapezoid I There are 2 pairs of congruent angles. Review Grade 5 (MA.5.G.5.3) 3. How many kilograms are equal to 4. Which measurement is more precise? 5,000 grams? A 500 kilograms B 50 kilograms C 5 kilograms D 0.5 kilogram 6 1 G 3__ inches 4 __ feet H 31 2 I 4 feet (MA.4.A.6.4) 5. What is the greatest common factor of 20 and 35? 6. How many factors do in common? A 3 F 1 B 4 G 2 C 5 H 3 D 6 I 4 P252 54 and 56 have © Houghton Mifflin Harcourt Look Back __ inches F 31 Lesson 7 Name MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Three-Dimensional Solids Classify each solid. Write prism, pyramid, cone, cylinder, or sphere. 1. 2. 3. There are no edges, vertices, or flat faces. It is a sphere ____. ____ ____ Name the solid. 4. 5. ____ 7. 6. ____ 8. ____ 9. ____ 10. Darrien is making a solid out of folded paper. © Houghton Mifflin Harcourt ____ ____ 11. Nanako said she drew a square pyramid His solid has six congruent faces that are all squares. What type of solid did he make? and that all of the faces are triangles. Is this possible? Explain. ______ ______ Chapter 10 P253 Lesson Check (MA.5.G.3.1) 1. Which of the following has exactly four faces? 2. Which of the following does NOT have any rectangular faces? A cone F pentagonal prism B square G hexagonal pyramid C triangular prism H rectangular prism D triangular pyramid I square pyramid Review Grade 5 (MA.5.G.5.3) 3. How many seconds are in 15 minutes? 4. Which unit is more precise? A 1,500 F gallons B 1,200 G quarts C 900 H pints D 150 I cups (MA.5.G.3.1) 5. How many sides does a heptagon have? 6. How many sides does a pentagon have? A 5 F 3 B 6 G 5 C 7 H 7 D 8 I 9 P254 © Houghton Mifflin Harcourt Look Back Lesson 8 Name MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Faces, Edges, and Vertices Name the solid. Then identify the number of faces, edges, and vertices it has. 1. 2. 3. There are two triangular bases; it is a triangular prism ____ 5 Edges: _ 9 Faces: _ 6 Vertices: _ © Houghton Mifflin Harcourt 4. ____ ____ Faces: _ Edges: _ Faces: _ Edges: _ Vertices: _ Vertices: _ 5. 6. ___ ___ ___ Faces: _ Edges: _ Faces: _ Edges: _ Faces: _ Edges: _ Vertices: _ Vertices: _ Vertices: _ 7. Name a solid that has no edges or vertices. 8. Consider a pentagonal prism. Identify the number of faces, edges, and vertices. _______ _______ Chapter 10 P255 Lesson Check (MA.5.G.3.1) 1. Which of the following solids has exactly 2. Which of the following does NOT have any edges? six faces? A cube F cube B sphere G sphere C triangular prism H rectangular prism D triangular pyramid I square pyramid Review Grade 5 (MA.5.G.5.3) 3. Which of the following measures is greater 4. Which unit is more precise? than 3 meters? A 0.0037 kilometer F centigrams B 28 decimeters G milligrams C 250 centimeters H decigrams D 2900 millimeters Look Back I grams (MA.4.A.1.2) 5. What is the product of 38 and 4,000? 6. What is the best estimate for the product of 49 and 23? F 1,000 B 152,000 G 800 C 15,200 H 100 D 1,520 I 80 © Houghton Mifflin Harcourt A 1,520,000 P256 PROBLEM SOLVING Name Search for Patterns • Faces, Edges, and Vertices Lesson 9 MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Solve each problem using the picture below. Row 1 Row 2 1. How many hexagonal tiles will be in the 9th row? The number of hexagonal tiles in the row equals the row number. The 9th row will have: 9 hexagonal tiles ____. 2. How many triangular tiles will be in the 9th row? ____ $0.50. Hexagonal tiles cost $1.00. How much will it cost to make the 9th row 3. Triangular tiles cost of tiles? ____ 4. How much will it cost to make the first 9 rows of tiles? ____ 5. How many balls of clay and straws are needed © Houghton Mifflin Harcourt to make a hexagonal pyramid? ____ 6. What is the least number of balls of clay and straws needed to make a cube? ____ Chapter 10 P257 Lesson Check 1. Denisha used (MA.5.G.3.1) 9 balls of clay and 16 straws to make a solid pyramid. How many faces does the solid have? A 6 B 7 2. Two hexagons can be drawn so that they share one side. A third hexagon can be drawn to share one side with only one of the existing hexagons. If this pattern continues, how many sides will be drawn for 10 hexagons? C 8 F 16 D 9 G 50 H 51 I 60 Review Grade 5 (MA.5.G.5.2) 3. How many decimeters are in 300 meters? 4. How many quarts are in A 30,000 decimeters F 30 quarts B 3,000 decimeters G 60 quarts C 30 decimeters H 120 quarts D 3 decimeters I 150 quarts (MA.4.A.1.2) 5. What is the product of 24 and 19? 6. Which is the best estimate for the product of 1,961 and 41? A 210 F 80,000 B 240 G 8,000 C 426 H 500 D 456 I 50 P258 © Houghton Mifflin Harcourt Look Back 15 gallons? Lesson 10 Name MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Model Three-Dimensional Solids Draw a net for the given solid. 1. Hexagonal pyramid 2. Cylinder 3. Triangular pyramid 5. 6. . Identify the solid from its net. 4. © Houghton Mifflin Harcourt ____ ____ 7. Draw the net of a cube that has a side length of 15 mm. ____ 8. Draw the net of a rectangular prism that has a length of 25 mm, a width of 12 mm, and a height of 20 mm. Chapter 10 P259 Lesson Check (MA.5.G.3.1) 1. The net of what solid is made of six 2. Which of the following solids has 5 faces? congruent squares? A square pyramid F triangular pyramid B triangular pyramid G rectangular prism C sphere H cylinder D cube I rectangular pyramid Review Grade 5 (MA.5.G.5.2) 3. How many days are in 208 weeks? 4. How many fluid ounces are in A 1,460 F 16 fluid ounces B 1,245 G 32 fluid ounces C 400 H 48 fluid ounces D 120 I 96 fluid ounces (MA.4.A.1.2) 5. What is the product of A 210 B 240 C 426 D 434 P260 31 and 14? 6. Which is the best estimate for the product of 1,162 and 78? F 80,000 G 8,000 H 500 I 50 © Houghton Mifflin Harcourt Look Back 3 quarts? Lesson 11 Name MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Views of Three-Dimensional Solids Name the solid figure that has the given views. 1. 2. kfg ]ifek kfg j`[\ The view from the top shows the base is a circle. The view from the side shows the lateral faces are triangles. So, the shape is a cone. ____ ]ifek j`[\ _____ _____ Draw the front, top, and side views of each solid figure. 3. Hexagonal pyramid 4. Triangular pyramid 5. Rectangular prism 6. Pentagonal pyramid 7. The builders of a new construction project 8. Draw the front, top, and side view for a © Houghton Mifflin Harcourt look at the floor plan before they begin. Name the solid shown in the floor plan. kfg ]ifek possible roof for the building. Then name the solid. j`[\ _______ _______ Chapter 10 P261 Lesson Check (MA.5.G.3.1) 1. Which of the following shows the top view of the pyramid below? the prism below? A C B D Review Grade 5 2. Which of the following shows the top view of F H G I (MA.5.G.5.2) 3. How many decimeters are in 4. How many quarts are in 5,000 meters? A 500,000 decimeters F 4 quarts B 50,000 decimeters G 12 quarts C 500 decimeters H 40 quarts D 50 decimeters I 120 quarts (MA.4.A.1.2) 5. What is the product of 31 and 22? 6. What is the best estimate for the product of 3,153 and 69? A 53 F 210,000 B 62 G 21,000 C 651 H 2,100 D 682 I 210 P262 © Houghton Mifflin Harcourt Look Back 10 gallons? MA.5.G.5.3, MA.5.G.3.1 Name Chapter 10 Extra Practice Lesson 10.1 (pp. 437–440) Find the measure of /X in each figure. 1. N 2. Q 3. O Q P O P O N Q P Use a protractor to draw each angle. 4. 60° 5. 170° Lesson 10.2 (pp. 441–444) Write whether the two figures are congruent or not congruent. 1. 8 /Zd 9 -' ; /Zd /Zd -' -' /Zd : /Zd -' -' -' < 2. /Zd = Lesson 10.3 (pp. 445–448) Solve. © Houghton Mifflin Harcourt 1. Will has the hexagon at the right. He wants to show that all sides are congruent and all angles are congruent, but he doesn’t have a ruler or protractor. How can he show this? Chapter 10 P263 Lesson 10.4 (pp. 449–452) Name each polygon. Then tell if it is a regular polygon or not a regular polygon. Measure to check your answer. 1. 2. Lesson 10.5 (pp. 453–456) Classify each triangle. Write isosceles, scalene, or equilateral. Then write right, acute, or obtuse. 1. 2. ,p[ ,p[ ,p[ 3. +Zd ,Zd ()d ()d *Zd +d Lesson 10.6 (pp. 457–460) Classify each quadrilateral in as many ways as possible. Write quadrilateral, parallelogram, rectangle, rhombus, square, or trapezoid. 2. © Houghton Mifflin Harcourt 1. P264 MA.5.G.5.3, MA.5.G.3.1 Name Chapter 10 Extra Practice Lesson 10.7 (pp. 463–466) Name the solid figure. 1. 2. 3. Lesson 10.8 (pp. 467–470) Name the solid figure. Then identify the number of faces, vertices, and edges it has. 1. 2. 3. Faces: _ Edges: _ Faces: _ Edges: _ Faces: _ Edges: _ Vertices: _ Vertices: _ Vertices: _ Lesson 10.9 (pp. 471–474) Solve. © Houghton Mifflin Harcourt 1. Sonia counts the faces on a cube. Then, she connects a cube and counts the faces that she can see on the two cubes. How many faces will be visible if she ends up with a row of 5 cubes? Chapter 10 P265 Lesson 10.10 (pp. 475–478) Identify the solid figure from its net. 1. 2. 3. 4. Lesson 10.11 (pp. 479–482) Name the solid figure that has the given views. 1. 2. ]ifek kfg ]ifek j`[\ kfg j`[\ Each solid is made with six cubes. Draw a top view, a front view, and a side view for each solid figure. 3. 4. © Houghton Mifflin Harcourt 5. P266