# Points, Lines, Rays, And Angles

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Points, Lines, Rays, and AnglesDear Family,This week your child is learning about points, lines,rays, and angles.30Here are some vocabulary words that tell about the geometry concepts thatyour child is learning.AA point is a single location in space.Point A is shown at the right.A line segment is a straight row of pointsthat starts at one point and ends at another··.point. Line segment AB is written as  ·AB  AA line is a straight row of points thatgoes on forever in both directions.AB  .Line AB is written as  ·kBABlA ray is a straight row of points thatstarts at one point and goes on foreverin one direction. Ray AB is written as AB  . ·ABlAn angle is formed by two rays, lines, or linesegments that meet at a common pointcalled the vertex. The angle shown at the rightcan be named /A, /CAB, or /BAC.CABParallel lines are always the samedistance apart and never cross.Perpendicular lines cross to forma right angle.Invite your child to share what he or she knows about points, lines, rays, andangles by doing the following activity together. Curriculum Associates, LLC Copying is not permitted.Lesson 30 Points, Lines, Rays, and Angles643

ACTIVITYPoints, Lines, Rays, and AnglesDo this activity with your child to identify lines, rays, and angles.Together with your child, find examples of real-life objects that have parts thatlook like lines, rays, and angles. Give clues to describe the objects to each other without naming the objects.Use some of the geometry vocabulary words that your child is learning about. Try to guess each object from the other person’s description of it. Here are some real-life examples you might use:Guitar strings(parallel line segments)Ceiling fan (angles andline segments)644Lesson 30 Points, Lines, Rays, and AnglesBrick wall (perpendicular andparallel line segments)Fence (angles, parallel andperpendicular line segments) Curriculum Associates, LLC Copying is not permitted.

Angles31Dear Family,This week your child is learning to measure anddraw angles.Your child is learning how to find an angle’s exact measure.Before measuring an angle, it is helpful to estimate the measure by usingbenchmarks, such as a right angle and a straight angle. For example, to estimatethe measure of the blue angle below, compare it to a right angle and to astraight angle.90 angle180 angleA right angle has a measure of 90 degrees. A straight angle has a measureof 180 degrees. The measure of the blue angle is between 90 degrees and180 degrees.To find the exact measure of the angle, your child is learning to use a tool calleda protractor. Read the mark on the protractor thatthe other ray passes through.20 300 10 160150 1 40180 17040 50130 Then line up one ray with the 08 mark.100 110 12080 0 90 80 70 60 5130 10 4070 0 1040160 20 110 mark18070 001 016 10 2015 30 Line up the center point of the protractorwith the vertex of the angle.vertexThe angle measures 1308. (The ray also passes through the 508 mark,but since the angle is bigger than a 908 angle, the measure is not 508.)Invite your child to share what he or she knows about measuringand drawing angles by doing the following activity together. Curriculum Associates, LLC Copying is not permitted.Lesson 31 Angles671

ACTIVITYMeasuring AnglesDo this activity with your child to estimate the measure of angles. Identify angles in and around your home or outside in the yard or neighborhood. Youcan also look through magazines or newspapers for pictures that show angles.Here are some examples of angles you might find (or make):Angles formed by the handson a clock or watchAngles made bya bicycle frameAngles formed by fingersor by the bend of an elbow Estimate the measure of each angle by using right angles (such as the corner of a sheetof paper) and straight angles (such as the side of a sheet of paper) as benchmarks.Look for other real-world opportunities to estimate angle measures with your child.672Lesson 31 Angles Curriculum Associates, LLC Copying is not permitted.

Add and Subtract with AnglesDear Family,This week your child is learning to add and subtractwith angles.The two shapes at the right are placed together as shown.Two angle measures are given: 1088 and 558.Since there are no gaps and no overlaps between the shapes,you can add the two angle measures together to find themeasure of the larger angle formed by the two angles inthe shapes.32108 55 ?1088 1 558 5 1638The larger combined angle measures 1638.Your child is also learning to use subtraction to find angle measures. In the exampleabove, if the measure of the larger angle was given and the measure of one of theother angles was unmarked, your child could subtract to find the measure of theunmarked angle.For example, 1638 2 1088 5 558.Invite your child to share what he or she knows about adding and subtractingangles by doing the following activity together. Curriculum Associates, LLC Copying is not permitted.Lesson 32 Add and Subtract with Angles693

ACTIVITYADDING with AnglesDo this activity with your child to add angles.Materials sheet of paper, scissors Cut out a piece from a rectangular sheet of paper. Cut at an angle. Estimate the measure of the angle at the bottom of the piece you cut.For example, estimate that the angle measures about 50 degrees. Then estimate the measure of the angle at the bottom cornerwhere you cut the sheet of paper. For example, estimate that the anglemeasures about 130 degrees. Now put the two pieces of paper back together. Add the estimates of theangle measures in order to find the measure of the angle formed bycombining both angles. For example, 508 1 1308 5 1808. Ask your child to explain how you know the measure of the combined angleis 180 degrees. (Both angles combine to form a straight angle, which has ameasure of 1808.)694Lesson 32 Add and Subtract with Angles Curriculum Associates, LLC Copying is not permitted.

Classify Two-Dimensional Figures33Dear Family,This week your child is learning to classifytwo-dimensional shapes.Shapes can be sorted into groups based on the kinds of sides they have and thekind of angles they have. Some shapes your child is classifying are triangles;quadrilaterals such as squares, rhombuses, trapezoids, and parallelograms;and hexagons.ABCDOne way to classify shapes is by the kinds of sides they have. Shapes A and C have parallel sides and perpendicular sides. Shapes B and D have parallel sides only.Another way to classify shapes is by the kinds of angles they have. Shapes A and C have all right angles. Shape B has some acute angles and some obtuse angles. Shape D has all obtuse angles.Triangles can be classified by their sides and angles. Triangle E is a scalene triangle. It has no sidesthe same length. Triangle F is a right triangle. It has a right angle.FEInvite your child to share what he or she knows about classifyingtwo-dimensional figures by doing the following activity together. Curriculum Associates, LLC Copying is not permitted.Lesson 33 Classify Two-Dimensional Figures715

ACTIVITYCLASSIFYING Two-Dimensional FIGURESDo this activity with your child to classify two-dimensional figures. Use the grid of dots below or make a dot grid on another sheet of paper. One person draws a shape. The shape could be a triangle, a quadrilateral,or another kind of shape with straight sides. The other person describes the shape. Be sure to talk about any parallelsides and perpendicular sides that the shape has. Describe the anglesof the shape, too! Then name the shape. Switch roles. Take turns drawing a shape and describing and naming it.716Lesson 33 Classify Two-Dimensional Figures Curriculum Associates, LLC Copying is not permitted.

Symmetry34Dear Family,This week your child is learning about symmetry.You can find symmetrical shapes in real life, in both natural and man-made objects.A line of symmetry is a line that divides a shape into two mirror images.Your child is learning to identify lines of symmetry in shapes.The horizontal linedivides the oval intotwo matching parts.It is a line of symmetry.The vertical line dividesthe oval into twomatching parts. It isalso a line of symmetry.Your child is also learning to draw lines of symmetry. One way to do that isto imagine folding a shape in different ways.To draw lines of symmetry in this shapeforming a plus sign, imagine each wayit could be folded to form matching parts.Invite your child to share what he or she knows about symmetryby doing the following activity together. Curriculum Associates, LLC Copying is not permitted.Lesson 34 Symmetry743

ACTIVITYSymmetryDo this activity with your child to explore symmetry. Look together at the shapes below. Discuss which shapes you think haveat least one line of symmetry. Describe to each other where the line(s) of symmetry could be drawn. Have your child draw the lines of symmetry on the shapes. Carefully cut out each shape and fold the shape along the line(s) of symmetrythat your child drew. Talk about whether each line divides the shape into two matching parts.Answers: rectangle: 1 horizontal and 1 vertical line of symmetry; square with curved corners: 1 horizontal and 1 vertical line ofsymmetry, 2 diagonal lines of symmetry; smiley face: 1 vertical line of symmetry; block with arrow: 1 horizontal line of symmetry744Lesson 34 Symmetry Curriculum Associates, LLC Copying is not permitted.

Before measuring an angle, it is helpful to estimate the measure by using benchmarks, such as a right angle and a straight angle. For example, to estimate the measure of the blue angle below, compare it to a right angle and to a straight angle. 90 angle 180 angle A right angle has a measure of 90

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