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Geometry and Measurement of Plane Figures Activity Set 3 Trainer Guide geometry and measurement of Plane figures—Activity Set 3 Mid_PGe_03_TG Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF Plane FIGURES Activity Set 3 NGSSS 6.A.2.1 NGSSS 6.A.2.2 NGSSS 7.A.1.1 It’s Like This In this activity, participants will distinguish between similar and congruent plane figures using ratios. Materials • Transparency/Page: It’s Like This • Transparency/Page: It’s Like This Answer Key • Transparency/Page: Image Dilation • Transparency/Page: Similar Sides • Transparency/Page: Similar Sides Answer Key • blank transparencies • ruler with centimeters (1 for each participant) • protractor (1 for each participant) Vocabulary • congruent figures • similar figures • dilation • scale factor Time: 20 minutes Introduce it’s like this Measure the angles and sides of each figure and label the diagrams. B E H Fig. 1 A Fig. 2 C D F Fig. 3 G •Explain to participants that they will investigate the relationships between similar figures and congruent figures. I •Display Transparency: It’s Like This and have participants take out their matching pages. 1. How are Figures 1 and 2 the same? How are Figures 1 and 2 different? 2. How are Figures 1 and 3 the same? How are Figures 1 and 3 different? geometry and measurement of Plane figures—activity set 3 Trans_MS_PG_03 2 Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Transparency: It’s Like This •Instruct participants to use their protractors and rulers to measure and compare the three triangles on the page. •Direct participants to write the measurements on the figures and then describe the relationships between Figures 1 and 2 and Figures 1 and 3. geometry and measurement of Plane figures—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_TG 1 GEOMETRY AND MEASUREMENT OF Plane FIGURES Activity Set 3 •Ask participants to work individually. •Allow participants 5–7 minutes to complete the activity. Discuss and Do •Call the group together. •Ask volunteers to share their angle and length measurements for each figure. •Record the measurements on the transparency. •Ask volunteers to share their findings to the following questions: How are Figures 1 and 2 the same? (They are the same size and shape; all corresponding angles and all corresponding sides are equal.) ◆ How are they different? (They are exactly the same.) ◆ •Explain to participants that figures that are exactly the same size and same shape are congruent. •Write, on the transparency, ABC DEF, and point out that this means that the two triangles are congruent. •Ask volunteers to share their findings to the following questions: How are Figures 1 and 3 the same? (They are the same shape; the corresponding angles are the same size.) ◆ How are they different? (The corresponding sides are of different lengths.) ◆ •Tell participants that figures that are the same shape and have congruent angles, but that have corresponding side lengths that are proportional rather than equal, are similar. •Write, on the transparency, ABC GHI and point out that this means the two triangles are similar. geometry and measurement of Plane figures—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_TG 2 GEOMETRY AND MEASUREMENT OF Plane FIGURES Activity Set 3 •Draw, on a blank transparency, two similar triangles as illustrated below. •Tell participants that these triangles are similar. m 2c m m 3c 2c 3c m •Ask participants what observations can be made about these triangles. (Their corresponding angles are congruent and their corresponding sides are proportional.) 2cm 3cm •Draw another pair of similar triangles as illustrated below. Note: The angles are labeled for these scalene triangles. Side measures are rounded to the nearest tenth and angle measures are rounded to the nearest degree. •Ask participants if these triangles are similar. (yes) 55° 96° 4.7 6m 6.3 96° m 29° 4m 3m •Ask participants how they can tell that these triangles are similar. (Their corresponding angles are congruent and their corresponding sides are proportional.) 55° m 29° 8m geometry and measurement of Plane figures—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_TG 3 GEOMETRY AND MEASUREMENT OF Plane FIGURES Activity Set 3 Teaching Tip: Ask participants if all rectangles are similar, as they all have congruent corresponding angles. (No, their sides may not be in proportion to each other. Different rectangles may have different shapes, even though all angles are congruent. Squares, however, are always similar because their sides are always proportional.) image Dilation •Display Transparency: Image Dilation •Explain to participants that you can enlarge the image by creating a larger space that is proportional to this one. •Explain to participants that this process is often used by artists and craftspeople to enlarge a sketch to its full size when producing a painting or a mural. geometry and measurement of Plane figures—activity set 3 Trans_MS_PG_03 Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Transparency: Image Dilation •Demonstrate how to create a proportional grid by drawing a new box below the existing image. Make it with a scale factor of 2 : 1. The new box will be twice as wide and twice as tall. •Point out a small section of the image and sketch the part contained in the section into the corresponding section in larger grid by using the 2 : 1 ratio for each line. •Have students complete the process on their pages. •Allow 5–7 minutes for this activity. •Get the group’s attention. •Explain to participants that when proportions are used to create images larger or smaller than their originals, the proportions are referred to as scale factors. When a copy is five times the size of the original, it has been increased by a scale factor of 5. geometry and measurement of Plane figures—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_TG 4 GEOMETRY AND MEASUREMENT OF Plane FIGURES Activity Set 3 •Ask participants to describe the relationship between the height of the original and that of the copy. (The copy is twice as long. In terms of a ratio, the height of copy: height of original is 2 : 1. •Ask participants what the scale factor is. (2) •Ask volunteer participants how the area of the copy compares to the area of the original. (The copy is 4 times the area of the original. In terms of a ratio, area of copy : area of original is 4 : 1. •Explain that this scale factor is often expressed as 22 to indicate that it refers to area or square units. Conclude Similar Sides 1. ABC ~ DEF. Find the length of DF. •Display Transparency: Similar Sides and have participants take out their matching pages. B 150 150 A 120 •Have participants work in pairs. E 50 50 C D x F 2. Rectangle M is similar to rectangle N. The ratio of rectangle N’s width to rectangle M’s width is 3:2. Rectangle M has a length of 24 cm and a width of 16 cm. What is the perimeter of rectangle N? M N geometry and measurement of Plane figures—activity set 3 Trans_MS_PG_03 Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Transparency: Similar Sides •Tell participants to use what they have learned about ratios to find the missing dimensions of the figures on their pages. •Allow 5–7 minutes for this activity. •Call the group together. •Ask for volunteers to share their processes and their findings. Write the steps for each solution on the displayed transparency. •Refer to Transparency: Similar Sides Answer Key to resolve any questions. End of It’s Like This geometry and measurement of Plane figures—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_TG 5 GEOMETRY AND MEASUREMENT OF Plane FIGURES Activity Set 3 Race to Place In this activity, participants will use geometric knowledge that they remember to match pictures of angles and shapes with their definitions. Materials • Transparency/Page: Race to Place Directions • Transparency/Page: Triangle Facts Answer Key • Transparency/Page: Angle Facts Answer Key • Transparency/Page: Angles in Shapes Answer Key • Transparency/Page: Line Facts Answer Key • Transparency/Page: Circle Facts Answer Key • Race to Place Cards • 5 pocket charts • bell Time: 15 minutes Teaching Tip: Post the pocket charts with their titles and the definitions before the beginning of the activity. Use the Facts transparencies as a guide for the definitions that go with each title. Space the charts around the room with a lot of room between them. geometry and measurement of Plane figures—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_TG 6 GEOMETRY AND MEASUREMENT OF Plane FIGURES Activity Set 3 Introduce •Suggest to participants that over time they have accumulated a lot of knowledge about the way lines, shapes, and angles work. •Point out the five charts and their definitions. •Explain to participants that they will compete as teams to match geometric definitions with pictures that illustrate the concepts defined. Teaching Tip: If you have a large group, assign pairs instead of single people to each card. DISCUSS AND DO race to place Directions • Distribute your team cards evenly among the members of your team. • Have team members play their cards in relay fashion. • Have a player: • race to the chart that holds the definition of the picture on his or her card •Display Transparency: Race to Place Directions. •Go over the steps of the game. •Have participants move into 4 or 5 equal-sized groups. • place the card next to the definition • race back to the team and sit down • Have the next person race to the chart and place his or her card. • Have one team member race to the front and ring the bell when all the team’s cards are correctly placed. •Distribute the cards—all of one colored shape to each group, one card per person. •Call, “Go.” •Have the first group to finish send one member to the front of the room to ring the bell. geometry and measurement of Plane figures—activity set 8 TRANS_MS_PG_08 Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Transparency: Race to Place Directions Teaching Tip: If a team member cannot place his or her card, he or she should go to the end of the line and wait to place the card after other team members have placed their cards. Teaching Tip: If the group is inexperienced, permit them a few moments to look at the definition sheets (Answer Keys) before the game. geometry and measurement of Plane figures—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_TG 7 GEOMETRY AND MEASUREMENT OF Plane FIGURES Activity Set 3 Conclude •Congratulate participants for being able to remember so many geometry concepts and definitions. •Display the answer key transparencies in turn, quickly reviewing the definitions. •Emphasize the following definitions for each key (these will be of use in subsequent activities): triangle Facts Answer Key • A scalene triangle has no congruent sides and no congruent angles. ◆ • An isosceles triangle has two congruent sides and two congruent angles. • An equilateral triangle has three congruent sides and three congruent angles. ◆ • The angles of an acute triangle are all less than 90˚. • One angle in an obtuse triangle is greater than 90˚. ◆ • A right triangle has one angle equal to 90˚. The side opposite the 90˚ angle is called the hypotenuse. Transparency: Triangle Facts Answer Key –equilateral triangle –right triangle (esp. hypotenuse) Transparency: Angle Facts Answer Key –straight angle –vertical angles Transparency: Angles in Shapes Answer Key –triangle –equilateral triangle geometry and measurement of Plane figures—activity set 3 TRANS_MS_PG_03 Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Transparencies: Triangle Facts, Angle Facts, Angles in Shapes, Line Facts, and Circle Facts Answer Keys ◆ ◆ Transparency: Line Facts Answer Key –alternate interior angles Transparency: Circle Facts Answer Key –circumference End of Race to Place geometry and measurement of Plane figures—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_TG 8 It’s Like This Measure the angles and sides of each figure and label the diagrams. B E H Fig. 1 A Fig. 2 C D F Fig. 3 G I 1.How are Figures 1 and 2 the same? How are Figures 1 and 2 different? 2.How are Figures 1 and 3 the same? How are Figures 1 and 3 different? GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM It’s Like This Answer Key Measure the angles and sides of each figure and label the diagrams. B E H 90º A 53º 37º 4 cm 3 cm Fig. 1 53º C Fig. 2 90º D 6 cm 3 cm 53º 37º 4 cm F Fig. 3 90º G 37º 8 cm I 1.How are Figures 1 and 2 the same? The angle and side measurements are exactly the same. How are Figures 1 and 2 different? They are not different. They are exactly the same. 2.How are Figures 1 and 3 the same? The angle measurements are exactly the same. How are Figures 1 and 3 different? The side measurements are different, but they are in proportion to each other. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Image Dilation GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Similar Sides 1. ABC ~ DEF. Find the length of DF. B 150 150 E 50 50 A 120 C D x F 2.Rectangle M is similar to rectangle N. The ratio of rectangle N’s width to rectangle M’s width is 3:2. Rectangle M has a length of 24 cm and a width of 16 cm. What is the perimeter of rectangle N? M N GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Similar Sides Answer Key 1. ABC ~ DEF. Find the length of DF. AC = DF AB DE 120 = 150 x 50 B 120 • 50 = 150x 150 6,000 = 150x 150 E 50 50 A 120 C D x F 6,000 = x 150 40 = x 2.Rectangle M is similar to length of N = l length of M = 24 rectangle N. The ratio of 2l rectangle N’s width to rectangle M’s width is 3:2. 2l Rectangle M has a length of l 24 cm and a width of 16 cm. width of N = w What is the perimeter of width of M = 16 rectangle N? 2w = 32 = 3 • 24 = 72 = 36 = 32 = 3 • 16 2w = 48 w = 24 M N P = 2l + 2w P = 2(36) + 2(24) P = 72 + 48 P = 120 cm GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Race to Place Directions •Distribute your team cards evenly among the members of your team. •Have team members play their cards in relay fashion. •Have a player: • race to the chart that holds the definition of the picture on his or her card • place the card next to the definition • race back to the team and sit down •Have the next person race to the chart and place his or her card. •Have one team member race to the front and ring the bell when all the team’s cards are correctly placed. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Triangle Facts Answer Key • A scalene triangle has no congruent sides and no congruent angles. • An isosceles triangle has two congruent sides and two congruent angles. • An equilateral triangle has three congruent sides and three congruent angles. • The angles of an acute triangle are all less than 90˚. • One angle in an obtuse triangle is greater than 90˚. • A right triangle has one angle equal to 90˚. The side opposite the 90˚ angle is called the hypotenuse. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Angle Facts Answer Key • The measure of an acute angle is less than 90˚. • The measure of an obtuse angle is greater than 90˚ and less than 180˚. • The measure of a straight angle is equal to 180˚. • The measure of a right angle is equal to 90˚. • Angles that share a common side between them are adjacent. • Two angles with measures that sum to 180˚ are called supplementary. • Nonadjacent angles formed by two intersecting lines are called vertical angles. They have the same measure. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Angles in Shapes Answer Key • A triangle has angles that sum to 180˚. • A rectangle has angles that sum to 360˚. • Angles inside a shape are interior angles. • Exterior angles are angles outside a shape that are formed by extending a side of the shape. • The base angles and opposite sides of an isosceles triangle are congruent. • The sides and angles of an equilateral triangle are congruent. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Line Facts Answer Key • A set of points, a straight path, that extends indefinitely in two opposite directions is a line. • A line segment is two endpoints and the straight path between them. • Perpendicular lines form right angles. • If a line intersects two parallel lines, the alternate interior angles are equal. • Parallel lines are equidistant from each other. 6 cm GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development 6 cm Mid_PGe_03_PM Circle Facts Answer Key • A complete revolution around the center of a circle has 360º. • A chord is a line segment that connects two points on the circumference of a circle. • The line segment joining the center of the circle and a point on its circumference is called a radius. • A diameter is a chord that passes through the center of a circle. Its length is twice that of the radius of the circle. • A circle is the set of all points in a plane that are equidistant from a specified point. • The distance around a circle is called its circumference. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Glossary Geometry and Measurement of Plane Figures acute angle An angle with a measure less than 90 degrees (°). angle A geometric figure composed of two raysor line segments that share the same endpoint,called a vertex. area The numberof square units in a region. circle The set of all points in a plane that are the same distance from a fixedpoint (the center of the circle). circumference The perimeter of (distance around) a circle. The circumference can befound using the formula C = 2πr,where C is the circumference of the circle and r is the radius of the circle. congruent figures Two figures that haveidentical size and shape so that when one is placed overthe other,theycoincide exactly. coordinate pair An ordered pair of numbersthat indicates the position of a point on a plane. The first numberof a coordinate pair givesthe point’s location in relation to the x-axis.The second numberin a coordinate pair givesthe point’s location in relation to the y-axis. coordinate plane A plane containing an x-axisand a y-axis.Everypoint on the plane can bedescribedusing a coordinate pair. degree (°) A unit of measure for angles. 1° is around a point. 1 360 of a complete revolution equilateral The propertyof havingequal,or congruent,sides. equilateral triangle A three-sided polygonwith all sides and with all angles congruent. hexagon A six-sidedpolygon. irregular polygon A polygonin which not all the sides are congruent and not all the angles havethe same measure. GEOMETRY AND AND MEASUREMENT MEASUREMENT OF OF PlANE Plane FIGURES—AcTIvITY FIGURES—ActivitySET Set13 BLM_MS_PG_01 Mid_PGe_03_PM Copyright© by 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development the McGraw-Hill Companies—McGraw-Hill Professional Development Glossary (continued) isosceles triangle A triangle that has two congruent sides and two congruent angles. line The set of all contiguous (touching) points that form a straight path extendingindefinitelyin two directions opposite each other. line segment A part of a straight line that has two end points and a fixedlength; a straight line segment marksthe shortest distance betweentwo points. linear unit A unit of measure for elements of a single dimension—length. obtuse angle An angle with a measure greater than 90° and less than 180°. parallel lines Lines that do not intersect and that are everywhere equidistant from each other. parallelogram A quadrilateral in which bothpairs of opposite sides are parallel. pentagon A five-sidedpolygon. perimeter The distance around the outside of a plane shape or figure. perpendicular At right angles to. Two lines are perpendicular if their intersection creates right angles. pi (π) The ratio of the circumference of anycircle to its diameter (3.141592653 . . .). Pi is usuallyrepresented bythe Greekletter,π. plane A flat surface that extendsforeverin all directions. plane figure A figure that lies entirelyin one plane. point A location in space. polygon A simple,closed plane shape composed of a minimum of three straight-line segments. GEOMETRY AND AND MEASUREMENT MEASUREMENT OF OF PlANE Plane FIGURES—AcTIvITY FIGURES—ActivitySET Set13 BLM_MS_PG_01 Mid_PGe_03_PM Copyright© by 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development the McGraw-Hill Companies—McGraw-Hill Professional Development Glossary (continued) quadrilateral A four-sided polygon. radius A segment connecting the center of a circle to anypoint on the circle; the length of the radius. ray A subsetof a line that includes one endpoint and that extendsinfinitely from that endpoint in one direction. rectangle A quadrilateral that includes four interior right angles. regular polygon A polygonin which all the sides are congruent and all the angles havethe same measure. rhombus A parallelogram in which all sides are congruent. right angle An angle with a measure of 90°. right triangle A triangle with one right angle. scalene triangle A triangle in which no sides are congruent and no angles havethe same measure. similar figures Figures that havecongruent corresponding angles and in which corresponding sides are proportional. square A quadrilateral in which all sides and all angles are congruent. square unit A unit of measure used to describethe surface (area) of figures of two dimensions—length and width. straight angle An angle with a measure of 180°. trapezoid A quadrilateral in which onlyone pair of sides is parallel. triangle A three-sided polygon. vertex (pl. vertices) The intersection point shared bytwo sides of a polygonor the two sides (rays)of an angle. Also the intersection point shared bythree or more edges of a polyhedron. GEOMETRY AND AND MEASUREMENT MEASUREMENT OF OF PlANE Plane FIGURES—AcTIvITY FIGURES—ActivitySET Set13 BLM_MS_PG_01 Mid_PGe_03_PM Copyright© by 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (1 of 20) GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Race to Place Cards (2 of 20) GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM 6 cm GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (3 of 20) 6 cm Mid_PGe_03_PM Race to Place Cards (4 of 20) GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Race to Place Cards (5 of 20) GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Race to Place Cards (6 of 20) GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Race to Place Cards (7 of 20) GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Race to Place Cards (8 of 20) GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Race to Place Cards (9 of 20) GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM Race to Place Cards (10 of 20) GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Mid_PGe_03_PM A chord is a line segment that connects two points on the circumference of a circle. The line segment joining the center of the circle and a point on its circumference is called a radius. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (11 of 20) A complete revolution around the center of a circle has 360º. Mid_PGe_03_PM Parallel lines are equidistant from each other. The measure of a right angle is equal to 90°. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (12 of 20) Ifa line intersects two parallel lines,the alternate interior angles are equal. Mid_PGe_03_PM A line segment has two endpoints. Perpendicular lines form right angles. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (13 of 20) A set of points that extend indefinitelyin two opposite directions is a line. Mid_PGe_03_PM The base angles and opposite sides of an isosceles triangle are congruent. The sides and angles of an equilateral triangle are congruent. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (14 of 20) Exterior angles are angles outside a shape that are formed by extending a side of the shape. Mid_PGe_03_PM A rectangle has angles that sum to 360˚. Angles inside a shape are interior angles. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (15 of 20) A triangle has angles that sum to 180˚. Mid_PGe_03_PM Angles that share a common side between them are adjacent. Two angles that sum to 180˚ are called supplementary. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (16 of 20) Nonadjacent angles formed by two intersecting lines are called vertical angles. They have the same measure. Mid_PGe_03_PM The measure of an obtuse angle is greater than 90˚ and less than 180˚. The measure of a straight angle is equal to 180˚. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (17 of 20) The measure of an acute angle is less than 90˚. Mid_PGe_03_PM Oneangle in an obtuse triangle is greater than 90˚. A right triangle has one angle equal to 90˚. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (18 of 20) The angles of an acute triangle are all less than 90˚. Mid_PGe_03_PM A circle is the set of all points in a plane that are equidistant from a specified point. The distance around a circle is called its circumference. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (19 of 20) The diameter is a chord that passes through the center of a circle. Mid_PGe_03_PM An isosceles triangle has two congruent sides and two congruent angles. An equilateral triangle has three congruent sides and three congruent angles. GEOMETRY AND MEASUREMENT OF Plane FIGURES—Activity Set 3 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development Race to Place Cards (20 of 20) A scalene triangle has no congruent sides and no congruent angles. Mid_PGe_03_PM