Skill. 69 Graph Ordered Pairs. (First Quadrant) Using Skill 69 COMMON ERRORS. 285 Holt Matemáticas. OBJECTIVE Graph ordered pairs (first quadrant)

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1 Skill Graph Ordered Pairs (First Quadrant) Using Skill OBJECTIVE Graph ordered pairs (first quadrant) Minutes Direct students attention to the definition at the top of the page. Work through the example with the students. Ask: Is the order of the coordinates important? (Yes, for example, (, ) is not the same as (, )) Emphasize the need to be careful writing the ordered pairs. The x-coordinate is first, then the y-coordinate. For students having difficulty remembering the order, point out that the variables in the ordered pair (x, y) are in alphabetical order. TRY THESE In Exercises, students determine where certain stores are located by moving right and up in a coordinate plane. Exercise,, (, ) Exercise,, (, ) Exercise Video Store PRACTICE ON YOUR OWN Review the example at the top of the page. In Exercises, students are guided to find the ordered pair for a point. In Exercises 0, students have to determine the coordinates of a particular point. CHECK Determine that the students can graph an ordered pair. Success is indicated by out of correct responses. Students who successfully complete the Practice on Your Own and Check are ready to move on to the next skill. COMMON ERRORS Students may transpose the coordinates. Stress that the x-coordinate is first and the y-coordinate is second. Students may count incorrectly. Have students count the lines and not the spaces between numbers. Students who made more than errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy on the next page. Holt Matemáticas

2 Optional Alternative Teaching Strategy Graphing Ordered Pairs OBJECTIVE Graph ordered pairs MATERIALS index cards with ordered pairs, graph paper 0 Minutes Prepare a set of cards with ordered pairs. The ordered pairs should match the number of rows and columns in the classroom. For example, if there are rows and columns the ordered pairs should not be larger than (, ). Arrange the classroom desks into rows and columns. As shown below. Shuffle the cards and distribute one per student. Tell the students that the classroom is a coordinate plane. Ask: Where is the starting point? (zero, origin) Where is the starting point on our coordinate plane? (Have a student stand at the (origin) zero point.) Have the student standing at the (origin) zero point read the ordered pair on the card and move to the location on their card. Stress the need to move right and up. Repeat this activity several times. When students show an understanding of moving to their location switch the activity around. Place a student somewhere on the grid and have another student describe how to get to them. When students show an understanding, have them try the exercise using graph paper and a pencil. Holt Matemáticas

3 Nombre Representar gráficamente pares ordenados (primer cuadrante) Un par ordenado es un par de números que se usan para ubicar un punto en un plano cartesiano. Ejemplo coordenada x coordenada y El primer número en el par representa la coordenada x. Te indica cuántas unidades hay que avanzar hacia la (, ) derecha sobre el eje x. El segundo número representa la coordenada y. Te indica cuántas unidades hay que avanzar hacia arriba sobre el eje y. Siempre empieza en 0. Halla el Correo en el plano cartesiano que se muestra. Siempre empieza en 0. Primero, avanza espacios hacia la derecha. Luego, avanza espacios hacia arriba. Par ordenado (,) 0 y Banco Biblioteca Zoológico Correo Parque Florería Estadio Tienda de video 0 0 x Inténtalo Usa el plano cartesiano que se muestra arriba para completar cada enunciado. Cuáles son las coordenadas para la Biblioteca? Primero avanza espacios hacia la derecha. Luego, avanza espacios hacia arriba. Par ordenado (, ). Cuáles son las coordenadas para el parque? Primero avanza espacios hacia la derecha. Luego, avanza espacios hacia arriba. Par ordenado (, ). Qué tienda está ubicada en (, )? Primero avanza espacios hacia la derecha. Luego, avanza espacios hacia arriba. Ir a siguiente página Holt Matemáticas

4 Nombre Practica por tu cuenta Razona: Para hallar el par ordenado para el punto A, empieza en 0. Avanza unidades hacia la derecha, luego avanza unidades hacia arriba. El par ordenado para el punto A es (, ). 0 y A 0 0 x Usa el plano cartesiano de la derecha. Completa. Escribe el par ordenado para cada punto. punto A Avanza unidades hacia la derecha. Avanza unidades hacia arriba. punto B Avanza unidades hacia la derecha. Avanza unidades hacia arriba. punto C Avanza unidades hacia la derecha. Avanza unidades hacia arriba. 0 y A B C D E G F H 0 0 x Usa el plano cartesiano que se muestra arriba. Escribe el par ordenado para cada punto. 0 punto D Comprueba punto A punto B punto C punto D punto E y 0 A B C 0 0 punto F Usa el siguiente plano cartesiano. Escribe el par ordenado para cada punto. Holt Matemáticas D x

5 Skill Identify Polygons Using Skill OBJECTIVE Name a polygon by the number of its sides and angles Minutes Review the definition of a polygon and then direct students attention to the example for Triangles. Ask: How many sides do all of the triangles have? () How many angles do all of the triangles have? () Have students contrast the isosceles, scalene, and equilateral triangles and tell the lengths of the sides of each triangle. Ask: What do you call a triangle that has all three sides the same length? (an equilateral triangle) What do you call a triangle that has just two sides the same length? (an isosceles triangle) How is a scalene triangle different from an equilateral or isosceles triangle? (A scalene triangle has no sides of equal length.) As you work through the descriptions of the other triangles, have students identify each type of angle in the triangles. In Quadrilaterals, point out the right angles and the congruent sides. When reviewing the last three polygons, students should make note of the number of sides. Emphasize the meaning of root words to help students remember the names: gon, means angle; penta- means, hexa-, and octa-. Have students count the number of angles in each polygon and compare it to the number of sides. Ask: Does each polygon have the same number of angles as it does sides? (yes) PRACTICE ON YOUR OWN As students review the example at the top of the page, have them identify the properties that give each polygon its name. CHECK Determine if the students can identify a square or rhombus, an isosceles triangle, a rectangle, and a parallelogram. Success is indicated by out of correct responses. Students who successfully complete the Practice on Your Own and Check are ready to move to the next skill. COMMON ERRORS Students may label a parallelogram without right angles as a rectangle. Students may label a right triangle as an acute triangle. Students may label a rhombus as a square or trapezoid, or a trapezoid as a parallelogram. Students may not recognize non-regular polygons. Students who made more than errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy on the next page. Holt Matemáticas

6 Optional Alternative Teaching Strategy Use Models to Identify Polygons OBJECTIVE Use models to distinguish and name each polygon by its properties MATERIALS index card, models of polygons: triangles, quadrilaterals, pentagons, hexagons, and octagons Minutes Distribute models to students and have them sort the polygons by the number of sides. Ask: How many groups do you have? () How many sides do the figures in each group have? (,,,, ) Have students point to the group of triangles. Ask them to sort the triangles by the lengths of the sides. If necessary have students use a ruler to measure the sides. Ask: How many triangles have three congruent sides? (Answers will vary.) Say: This is an equilateral triangle. How many triangles have two congruent sides? (Answers will vary.) Say: This is an isosceles triangle. How many triangles have a different length on each side? (Answers will vary.) Say: This is a scalene triangle. Emphasize that a triangle can be classified by its sides. A triangle with three congruent sides is equilateral. A triangle with two congruent sides is isosceles. A triangle with no congruent sides is scalene. Next, have the students use the corner of an index card to classify the angles in some of the triangles. Have them show you an example of a right angle, an obtuse angle, and an acute angle. Recall that the measure of an acute angle is less than the measure of a right angle, and the measure of an obtuse angle is greater than the measure of a right angle. Repeat this activity using the other polygon models. Have students state the name of each type of polygon. Holt Matemáticas

7 Nombre Identificar polígonos Un polígono es una figura plana cerrada formada por tres o más segmentos de recta. Los polígonos se clasifican según la cantidad de lados y ángulos. Recuerda: Un segmento de recta forma parte de una línea que está entre dos extremos. Triángulos Los triángulos son polígonos con lados y ángulos. Clasifica los triángulos por la longitud de sus lados o por la medida de sus ángulos. cm cm Isósceles lados son congruentes. Rectángulo un ángulo recto cm Escaleno Todos los lados tienen distinta longitud. Acutángulo tres ángulos agudos Equilátero Todos los lados son congruentes. Obtusángulo un ángulo obtuso cm Cuadriláteros Los cuadriláteros son polígonos con lados y ángulos. Hay distintos tipos de cuadriláteros. cm pies 0 cm cm pies pies pies Cuadrilátero general lados de cualquier longitud ángulos de cualquier medida yd yd yd yd Rectángulo pares de lados congruentes ángulos rectos Trapecio par de lados paralelos m m m m Rombo lados congruentes pares de ángulos congruentes Paralelogramo pares de lados congruentes pares de lados paralelos cm cm cm cm Cuadrado lados congruentes ángulos rectos Pentágono, hexágono, octágono Pentágono lados ángulos penta significa cinco pulg pulg pulg Octágono Hexágono lados ángulos hexa significa seis lados ángulos octa significa ocho pulg Ir a siguiente página Holt Matemáticas

8 Nombre Practica por tu cuenta TRIÁNGULOS CUADRILÁTEROS isósceles escaleno equilátero general trapecio paralelogramo pentágono hexágono rectángulo acutángulo obtusángulo rectángulo rombo cuadrado octágono Identifica cada triángulo. Elige triángulo isósceles, equilátero, rectángulo u obtusángulo. pulg pulg cm cm pies pies pulg cm pies Identifica cada cuadrilátero. Elige paralelogramo, rectángulo, rombo o trapecio. pulg yd mi mi pulg yd yd pulg yd mi mi pulg Identifica cada figura. 0 pulg pulg pulg pulg pulg pulg pulg pulg pulg pulg pulg Comprueba Identifica cada figura. pulg Holt Matemáticas

9 Skill Identify Congruent Figures Using Skill OBJECTIVE Identify congruent figures 0 Minutes Read about congruent figures at the top of the page. Explain to students that congruent figures have exactly the same size and shape. Look at the first set of figures. Ask: What are the geometric figures? (rectangles) How long are the rectangles? ( cm, cm) How wide are the rectangles? ( cm, cm) If the figures are both rectangles and they are the same length and the same width, what can you conclude about the rectangles? (They are congruent.) Focus on the second set of geometric figures. Be sure students understand the definition of congruent. The figures must be the same shape and the same size. Ask: What are the geometric figures? (squares) Since the figures are both squares, can you conclude that they are congruent? (No, they are not the same size.) Look at the third set of geometric figures. Make sure students know that when two polygons are congruent, their corresponding parts have the same measure. A congruence statement lists the corresponding angles in the same order. Ask: How do you know that the triangles are congruent? (By the congruence statement above the triangles.) What angle does angle C correspond to? (angle M) How do you know? (Because of the order of the congruence statement, C corresponds to M.) What side length does CD correspond to? (MN) How do you know? (Because of the order of the congruence statement, side CD corresponds to side MN.) TRY THESE Exercises require students to judge shape and size when deciding on congruence. Exercise requires students to identify corresponding parts of congruent figures. Exercise Congruent Exercise Not congruent Exercise A B Q R ; B C R S ; Q A PRACTICE ON YOUR OWN Review the examples at the top of the page. As they work through the exercises, remind students that the figures must be the same shape and size to be congruent. CHECK Determine if students know how to identify corresponding parts. Success is indicated by out of correct responses. Students who successfully complete the Practice on Your Own and Check are ready to move to the next skill. COMMON ERRORS Students may classify all squares as congruent because they are the same shape. Students may only look at one dimension when deciding whether shapes are the same size. Students might think that figures must have the same orientation to be congruent. Students who made more than errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy on the next page. Holt Matemáticas

10 Optional Alternative Teaching Strategy Model Congruent Figures OBJECTIVE Model identifying congruent figures MATERIALS scissors, worksheets with geometric figures, transparency of geometric figures 0 Minutes Distribute worksheets of geometric figures shown below to students. TRIANGLES equilateral isosceles QUADRILATERALS: trapezoid PENTAGONS rhombus scalene square regular not regular not regular HEXAGONS obtuse rectangle acute right parallelogram Ask: Which figures do you think are the same shape and the same size? (Answers may vary.) Cut one pair of congruent figures from the transparencies and demonstrate how to check for congruence by laying one on top of the other on an overhead projector. Repeat for a non-congruent pair. Have the students cut out their figures and check to see which pairs are congruent and which are not. Lead students to understand that the congruent figures are the same shape and size, and that the geometric figures that are not congruent are either not the same shape or not the same size. regular not regular not regular OCTAGONS regular not regular not regular Holt Matemáticas

11 Nombre Identificar figuras congruentes Las figuras congruentes tienen la misma forma y el mismo tamaño. Compara la forma y la longitud de los lados para decidir si las dos figuras son congruentes. Estas figuras tienen la misma forma y el mismo tamaño. cm cm Estas figuras tienen la misma forma, pero no tienen el mismo tamaño. m C CDE MNP M cm cm cm cm m m E D P N cm cm m Las figuras son congruentes. Las figuras no son congruentes. C M D N E P CD MN DE NP EC PM Inténtalo Completa. Decide si las dos figuras son congruentes. cm cm cm cm Misma forma? Mismo tamaño? cm cm cm cm Misma forma? Mismo tamaño? cm cm cm cm Completa los enunciados de congruencia. ABC QRS C A AB BC Q B S Q R Ir a siguiente página Holt Matemáticas

12 Nombre Practica por tu cuenta Razona: Las figuras congruentes tienen la misma forma y el mismo tamaño. m Congruentes m m m No congruentes m m Completa. Decide si las dos figuras son congruentes. Misma forma? Mismo tamaño? m m m m m m Misma forma? Mismo tamaño? 0 cm 0 cm cm cm 0 cm 0 cm cm cm cm 0 cm Misma forma? Mismo tamaño? 0 m m m m m cm cm cm cm cm cm cm cm cm 0 cm 0 cm cm 0 cm cm cm 0 cm Completa los enunciados de congruencia. DEF PRN D N P F D F E R E 0 E F N P R N Comprueba m m m m m m m m cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm Si STU JKL: Qué ángulo es correspondiente con el K? Qué lado es correspondiente con el L J? Holt Matemáticas