Geometry. vii. Houghton Mifflin Harcourt Publishing Company

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2 Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Lesson 98 CC.4.G. Lines, Rays, and Angles Lesson 99 CC.4.G. Parallel Lines and Perpendicular Lines Lesson 00 CC.4.G.2 Classify Triangles Lesson 0 CC.4.G.2 Classify Quadrilaterals Lesson 02 CC.4.G.3 Line Symmetry Lesson 03 CC.4.G.3 Find and Draw Lines of Symmetry vii

3 LESSON 98 Lines, Rays, and Angles OJECTIVE Identify and draw points, lines, line segments, rays, and angles. CC.4.G. Name What it looks like Think point D D A point names a location in space. line A; _ A line A; _ A A A line extends without end in opposite directions. line segment A; A line segment A; A A Segment means part. A line segment is part of a line. It is named by its two endpoints. ray MN; MN ray NM; NM M M N N A ray has one endpoint and extends without end in one direction. A ray is named using two points. The endpoint is always named first. angle XYZ; XYZ angle ZYX; ZYX angle Y; Y Y X Z Two rays or line segments that share an endpoint form an angle. The shared point is the vertex of the angle. A right angle forms a square corner. An acute angle opens less than a right angle. Draw and label an example of the figure.. PQ 2. K J An obtuse angle opens more than a right angle and less than a straight angle. Possible drawings are shown. 3. obtuse FGH A straight angle forms a line. H P Q K J F G Geometry 95

4 Lines, Rays, and Angles CC.4.G. Draw and label an example of the figure.. obtuse AC Possible drawings are shown. A Think: An obtuse angle is greater than a right angle. The middle letter,, names the vertex of the angle. C 2. GH 3. acute JKL 4. C L J K C Use the figure for 5 8. Possible answers are given. 5. Name a line segment. 6. Name a right angle. EF EJF C D E F G H 7. Name an obtuse angle. 8. Name a ray. CEJ JD J A Problem Solving Use the figure at the right for Classify AFD. obtuse 0. Classify CFE. right. Name two acute angles. Possible answers: AF and DFE 96 Lesson 98

5 LESSON 99 Parallel Lines and Perpendicular Lines OJECTIVE Identify and draw parallel lines and perpendicular lines. CC.4.G. Parallel lines are lines in a plane that are always the same distance apart. Parallel lines or line segments never meet. In the figure, lines A and CD, even if extended, will never meet. The lines are parallel. Write A CD. Lines AD and C are also parallel. So, AD C. Intersecting lines cross at exactly one point. Intersecting lines that form right angles are perpendicular. In the figure, lines AD and A are perpendicular because they form right angles at vertex A. Write AD A. Lines C and CD are also perpendicular. So, C CD. Use the figure for 3.. Name two sides that appear to be parallel. RV and ST 2. Name two sides that appear to be perpendicular. RV and RS or RS and ST 3. Name two sides that appear to be intersecting, but t perpendicular. RV and VT or TV and ST Geometry 97

6 Parallel Lines and Perpendicular Lines Use the figure for 3. CC.4.G.. Name a pair of lines that appear to be perpendicular. Think: Perpendicular lines form right angles. A and EF appear to form right angles. A and EF 2. Name a pair of lines that appear to be parallel. A and CD 3. Name ather pair of lines that appear to be perpendicular. EF and CD Draw and label the figure described. 4. MN and PQ intersecting at point R Possible drawings are shown. 5. WX YZ 6. FH JK P M R Q N Problem Solving Use the street map for Name two streets that intersect but do t appear to be perpendicular. Oak and Maple or Oak and irch 8. Name two streets that appear to be parallel to each other. Elm Oak Maple irch Maple and irch 98 Lesson 99

7 LESSON 00 Classify Triangles OJECTIVE Classify triangles by the size of their angles. CC.4.G.2 A triangle is a polygon with 3 sides and 3 angles. Each pair of sides joins at a vertex. You can name a triangle by its vertices. ΔPQR ΔQRP ΔRPQ ΔPRQ ΔQPR ΔRQP There are 3 have at least types of triangles. All triangles 2 acute angles. Obtuse triangle Right triangle Acute triangle one obtuse angle one right angle three acute angles P Q R acute acute acute. Name the triangle. Tell whether each angle is acute, right, or obtuse. A name for the triangle is ΔXYZ. X is acute. Y is obtuse. Z is acute. Classify each triangle. Write acute, right, or obtuse X Y Z right acute obtuse Geometry 99

8 Classify Triangles Classify each triangle. Write acute, right, or obtuse. CC.4.G.2. A C Think: Angles A and C are both acute. Angle is obtuse. obtuse 2. F 3. G J 4. L N D E H M right acute obtuse Problem Solving Check students drawings. 5. Use figure ACD below. Draw a line segment from point to point D. Name and classify the triangles formed. D A Possible answer: triangles AD and CD are both obtuse triangles. C 6. Use figure ACD below. Draw a line segment from point A to point C. Name and classify the triangles formed. D A Possible answer: triangles ADC and AC are both acute triangles. C 200 Lesson 00

9 LESSON 0 Classify Quadrilaterals OJECTIVE Sort and classify quadrilaterals. CC.4.G.2 A quadrilateral is a polygon with 4 sides and 4 angles. Some quadrilaterals have special names: Classify each figure as many ways as possible. Write trapezoid, parallelogram, rhombus, rectangle, or square trapezoid parallelogram, rectangle, rhombus, square parallelogram Geometry 20

10 Classify Quadrilaterals Classify each figure as many ways as possible. Write trapezoid, parallelogram, rhombus, rectangle, or square. CC.4.G.2. Think: 2 pairs of parallel sides 4 sides of equal length 0 right angles parallelogram, rhombus parallelogram, rectangle trapezoid quadrilateral parallelogram, rhombus Problem Solving 8. Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. What figure did Alan draw? trapezoid parallelogram 9. Teresa drew a quadrilateral with 2 pairs of parallel sides and 4 right angles. What quadrilateral could she have drawn? a rhombus a square or rectangle 202 Lesson 0

11 LESSON 02 Line Symmetry OJECTIVE Determine whether a figure has a line of symmetry. CC.4.G.3 Tell whether the parts on each side of the line match. Is the line a line of symmetry? Step Trace and cut out the shape. Fold the shape along the dashed line. Step 2 Tell whether the parts on each side match. Compare the parts on each side. match match The parts do t match. Step 3 Decide if the line is a line of symmetry. The parts on each side of the line do t match. So, the line is t a line of symmetry. Tell if the line appears to be a line of symmetry. Write or Geometry 203

12 Line Symmetry Tell if the dashed line appears to be a line of symmetry. Write or. CC.4.G Check students drawings. Complete the design by reflecting over the line of symmetry Problem Solving. Kara uses the pattern at the right to make paper dolls. The dashed line represents a line of symmetry. A complete doll includes the reflection of the pattern over the line of symmetry. Complete the design to show what one of Kara s paper dolls looks like. Check students drawing. 204 Lesson 02

13 LESSON 03 Find and Draw Lines of Symmetry OJECTIVE Identify and draw lines of symmetry in two-dimensional figures. CC.4.G.3 Tell whether the shape appears to have zero lines, line, or more than line of symmetry. Write zero,, or more than. Step Decide if the shape has a line of symmetry. Trace and cut out the shape. Fold the shape along a vertical line. Step 2 Decide if the shape has ather line of symmetry. Open the shape and fold it along a horizontal line. Step 3 Find any other lines of symmetry. Think: Can I fold the shape in other ways so that the two parts match exactly? Do the two parts match exactly? So, the shape appears to have Do the two parts match exactly? more than Tell whether the shape appears to have zero lines, line, or more than line of symmetry. Write zero,, or more than I can fold the paper diagonally two different ways, and the parts match exactly. line of symmetry. more than zero Geometry 205

14 Find and Draw Lines of Symmetry Tell whether the shape appears to have zero lines, line, or more than line of symmetry. Write zero,, or more than. CC.4.G more than zero more than Does the design have line symmetry? Write or. If your answer is, draw all lines of symmetry. Check students lines of symmetry Draw a shape for the statement. Draw the line or lines of symmetry. Check students drawings. 9. zero lines of symmetry 0. line of symmetry. 2 lines of symmetry Problem Solving Use the chart for Which number or numbers appear to have only line of symmetry? 3. Which number or numbers appear to have 2 lines of symmetry? 3 0 and Lesson 03