Skill. 69 Graph Ordered Pairs. (First Quadrant) Using Skill 69 COMMON ERRORS. 285 Holt Mathematics. 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, 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 Mathematics

2 Optional Alternative Teaching Strategy Graphing Ordered Pairs OBJECTIVE Graph ordered pairs MATERIALS index cards with ordered pairs, graph paper 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 Mathematics

3 Name Skill Graph Ordered Pairs (First Quadrant) An ordered pair is a pair of numbers used to locate a point on a coordinate plane. Example The first number in the pair represents the x-coordinate. It tells you how many units to move right on the x-axis. x-coordinate y-coordinate (, ) Try These Use the coordinate plane shown above to complete each statement. What are the coordinates for the Library. First move spaces right. Next, move spaces up. Ordered pair (, ) What are the coordinates for the Park? First move spaces right. Next, move spaces up. Ordered pair (, ) Skill What store is located at (, ). First move spaces right. Next, move spaces up. Go to the next side. The second number represents the y-coordinate. It tells you how many units to move up on the y-axis. Always start at 0. Find the Post Office on the coordinate plane shown. Always start at 0. First, move spaces to the right. Then, move spaces up. Ordered pair (, ) y Bank Library Zoo Park Post Office Florist Video Store Stadium 0 x Holt Mathematics

4 Name Practice on Your Own Think: To find the ordered pair for point A, start at 0. Move units to the right, then move units up. The ordered pair for point A is (, ). Skill y A Skill 0 x Use the coordinate plane at the right. Complete. Write the ordered pair for each point. point A Move units to the right. Move units up. point B Move units to the right. Move units up. point C Move units to the right. Move units up. y C A B D E G F H 0 x Use the coordinate plane above. Write the ordered pair for each point. point D Check point A point B point C point D point E Use the coordinate plane below. Write the ordered pair for each point. y A B C 0 point F Holt Mathematics 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 Mathematics

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 Mathematics

7 Name Skill Identify Polygons Skill A polygon is a closed plane figure formed by three or more line segments. Polygons are named by the number of their sides and angles. Triangles Triangles are polygons with sides and angles. Classify triangles by the lengths of their sides or by the measures of their angles. cm cm Isosceles sides are congruent. Right one right angle cm Scalene All sides are different lengths. Acute three acute angles Equilateral All sides are congruent. Obtuse one obtuse angle cm Quadrilaterals Quadrilaterals are polygons with sides and angles. There are different types of quadrilaterals. cm cm General Quadrilateral sides of any length angles of any size yds yds yds yds Rectangle pairs of congruent sides right angles ft cm ft ft Trapezoid pair of parallel sides m m m m Rhombus congruent sides pairs of congruent angles ft Parallelogram pairs of congruent sides pairs of parallel sides cm cm cm cm Square congruent sides right angles Remember: A line segment is part of a line between two endpoints. Pentagon, Hexagon, Octagon Pentagon sides angles penta means five Octagon sides angles octa means eight Hexagon sides angles hexa means six Go to the next side. Holt Mathematics

8 Name Skill Practice on Your Own Skill TRIANGLES QUADRILATERALS isosceles scalene equilateral general trapezoid parallelogram pentagon hexagon right acute obtuse rectangle rhombus square octagon Name each triangle. Choose isosceles, equilateral, right, or obtuse triangle. in. in. cm cm ft ft in. cm ft Name each quadrilateral. Choose parallelogram, rectangle, rhombus, or trapezoid. in. yd yd yd mi mi in. yd mi mi Name each figure. in. in. Check Name each figure. in. Holt Mathematics

9 Skill Identify Congruent Figures Using Skill OBJECTIVE Identify congruent figures 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 Mathematics

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 Mathematics

11 Name Skill Identify Congruent Figures Congruent figures have the same shape and the same size. Compare the shapes and the lengths of the sides to decide if the two figures are congruent. These figures have the same shape and the same size. cm cm These figures have the same shape, but do not have the same size. m m cm cm cm cm m m m m cm cm The figures are congruent. m m The figures are not congruent. Try These Complete. Decide if the two figures are congruent. cm cm cm cm Same shape? Same size? cm cm Same shape? Same size? cm cm cm cm cm cm Skill CDE MNP C M E D P N C M D N E P C D M N D E N P E C P M Complete the congruence statements. ABC QRS A Q C B S R A B B C Q Go to the next side. Holt Mathematics

12 Name Skill Practice on Your Own Think: Congruent figures have the same shape and the same size. m m Congruent m m m m Skill Not Congruent m m m m Complete. Decide if the two figures are congruent. Same shape? Same size? m m m m m m Same shape? Same size? cm cm cm cm cm cm cm cm cm cm Same shape? Same size? m m m m m m cm cm cm cm cm cm cm cm cm 0 cm 0 cm cm cm 0 cm 0 cm cm Complete the congruence statements. DEF PRN D N P F D F E R E E F N P R N Check m m m m m m m m cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm Given that STU JKL: What corresponds to K? What corresponds to L J? Holt Mathematics