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NameChapterDateFair Game Review3Tell whether the angles are adjacent or vertical. Then find the value of x.1.2.x 128 x 35 3.4.75 (2x 1) 4x 2x 5. The tree is tilted 14 . Find the value of x.14 x Copyright Big Ideas Learning, LLCAll rights reserved.Big Ideas Math BlueRecord and Practice Journal49

Name DateChapter3Fair Game Review (continued)Tell whether the angles are complementary or supplementary. Then findthe value of x.6.7.117 x 69 x 8.9.110 5x 41 x 10. A tributary joins a river at an angle. Find the value of x.50Big Ideas Math BlueRecord and Practice JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.1DateParallel Lines and TransversalsFor use with Activity 3.1Essential Question How can you describe angles formed by parallellines and transversals?1ACTIVITY: A Property of Parallel LinesWork with a partner. Discuss what it means for twolines to be parallel. Decide ona strategy for drawing twoparallel lines. Then draw thetwo parallel lines. Draw a third line thatintersects the two parallellines. This line is called atransversal.a. How many angles are formed by the parallel lines and the transversal?Label the angles.b. Which of these angles have equal measures? Explain your reasoning.Copyright Big Ideas Learning, LLCAll rights reserved.Big Ideas Math BlueRecord and Practice Journal51

Name Date3.12Parallel Lines and Transversals (continued)ACTIVITY: Creating Parallel LinesWork with a partner.a. If you were building thehouse in the photograph,how could you make surethat the studs are parallelto each other?Studsb. Identify sets of parallel lines and transversals in the photograph.3ACTIVITY: Using Technology to Draw Parallel Lines and a TransversalWork with a partner. Use geometrysoftware to draw two parallel linesintersected by a transversal.Fa. Find all of the angle measures.DGCAEBH52Big Ideas Math BlueRecord and Practice JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.1DateParallel Lines and Transversals (continued)b. Adjust the figure by moving the parallel lines or the transversalto a different position. Describe how the angle measures andrelationships change.What Is Your Answer?4. IN YOUR OWN WORDS How can you describe angles formed by parallellines and transversals? Give an example.5. Use geometry software to draw a transversal that is perpendicular to twoparallel lines. What do you notice about the angles formed by the parallellines and the transversal?Copyright Big Ideas Learning, LLCAll rights reserved.Big Ideas Math BlueRecord and Practice Journal53

Name Date3.1PracticeFor use after Lesson 3.1Use the figure to find the measures of the numbered angles.1.2.t1t34 21112 6a752a34bbComplete the statement. Explain your reasoning.at3. If the measure of 1 150 , then the measure of 6 .b214365874. If the measure of 3 42 , then the measure of 5 .5. If the measure of 6 28 , then the measure of 3 .6. You paint a border around the top of the wallsin your room. What angle does x need to be torepeat the pattern?54Big Ideas Math BlueRecord and Practice Journal154 x Copyright Big Ideas Learning, LLCAll rights reserved.

Name3.2DateAngles of TrianglesFor use with Activity 3.2Essential Question How can you describe the relationships among theangles of a triangle?1ACTIVITY: Exploring the Interior Angles of a TriangleWork with a partner.a. Draw a triangle. Label the interior angles A, B, and C.b. Carefully cut out the triangle. Tear off the three corners of the triangle.c. Arrange angles A and B so that they share a vertex and are adjacent.d. How can you place the third angle to determine the sum of the measuresof the interior angles? What is the sum?e. Compare your results with others in your class.f. STRUCTURE How does your result in part (d) compare to the rule youwrote in Lesson 1.1, Activity 2?Copyright Big Ideas Learning, LLCAll rights reserved.Big Ideas Math BlueRecord and Practice Journal55

Name Date3.22Angles of Triangles (continued)ACTIVITY: Exploring the Interior Angles of a TriangleWork with a partner.sa. Describe the figure.tDBEmACnb. LOGIC Use what you know about parallel lines and transversals to justifyyour result in part (d) of Activity 1.3ACTIVITY: Exploring an Exterior Angle of a TriangleWork with a partner.a. Draw a triangle. Label the interior angles A, B, and C.BDC45534672389101621112131415paper and extend one side toform exterior angle D, as shown.Ain.1c. Place the triangle on a piece ofcmb. Carefully cut out the triangle.d. Tear off the corners that are not adjacent to the56Big Ideas Math BlueRecord and Practice JournalCBexterior angle. Arrange them to fill the exteriorangle, as shown. What does this tell you aboutthe measure of exterior angle D?ACopyright Big Ideas Learning, LLCAll rights reserved.

Name3.24DateAngles of Triangles (continued)ACTIVITY: Measuring the Exterior Angles of a TriangleWork with a partner.Ea. Draw a triangle and label the interior and exterior anglesBas shown.Cb. Use a protractor to measure all six angles of your triangle.Complete the table to organize your results. What doesthe table tell you about the measure of an exterior angleof a triangle?FADExterior AngleD E F Interior AngleB A A Interior AngleC C B What Is Your Answer?5. REPEATED REASONING Draw three triangles that have different shapes.Repeat parts (b)–(d) from Activity 1 for each triangle. Do you get the sameresults? Explain.6. IN YOUR OWN WORDS How can you describe the relationships amongangles of a triangle?Copyright Big Ideas Learning, LLCAll rights reserved.Big Ideas Math BlueRecord and Practice Journal57

Name DatePractice3.2For use after Lesson 3.2Find the measures of the interior angles.1.2.x 70 84 32 x 3.4.115 50 x x x x Find the measure of the exterior angle.5.6.40 x 88 47 x 7. Find the value of x on the clothes hanger.110 x 58Big Ideas Math BlueRecord and Practice Journalx Copyright Big Ideas Learning, LLCAll rights reserved.

Name3.3DateAngles of PolygonsFor use with Activity 3.3Essential Question How can you find the sum of the interior anglemeasures and the sum of the exterior angle measures of a polygon?1ACTIVITY: Exploring the Interior Angles of a PolygonWork with a partner. In parts (a)–(e), identify each polygon and the numberof sides n. Then find the sum of the interior angle measures of the polygon.a. Polygon:Number of sides: n Draw a line segment on the figure that dividesit into two triangles. Is there more than one wayto do this? Explain.What is the sum of the interior angle measures ofeach triangle?What is the sum of the interior angle measures of the figure?b.c.d.e.Copyright Big Ideas Learning, LLCAll rights reserved.Big Ideas Math BlueRecord and Practice Journal59

Name Date3.3Angles of Polygons (continued)f. REPEATED REASONING Use your results to complete the table. Thenfind the sum of the interior angle measures of a polygon with 12 sides.Number of Sides, n345678Number of TrianglesAngle Sum, S2ACTIVITY: Exploring the Exterior Angles of a PolygonWork with a partner.a. Draw a convex pentagon. Extend the sides to formBthe exterior angles. Label one exterior angle at eachvertex A, B, C, D, and E, as shown.ACb. Cut out the exterior angles. How can you join thevertices to determine the sum of the angle measures?What do you notice?EDc. REPEATED REASONING Repeat the procedure in parts (a) and (b) foreach figure below.What can you conclude about the sum of the measures of the exterior anglesof a convex polygon? Explain.60Big Ideas Math BlueRecord and Practice JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.3DateAngles of Polygons (continued)What Is Your Answer?3. STRUCTURE Use your results from Activity 1 to write an expression thatrepresents the sum of the interior angle measures of a polygon.4. IN YOUR OWN WORDS How can you find the sum of the interior anglemeasures and the sum of the exterior angle measures of a polygon?Copyright Big Ideas Learning, LLCAll rights reserved.Big Ideas Math BlueRecord and Practice Journal61

Name DatePractice3.3For use after Lesson 3.3Find the sum of the interior angle measures of the polygon.1.2.3.Find the measures of the interior angles.4.135 x 120 80 5.120 x 120 x 135 Find the measure of each interior angle of the regular polygon.6.7.8. In pottery class, you are making a pot that is shaped as a regular hexagon.What is the measure of each angle in the regular hexagon?62Big Ideas Math BlueRecord and Practice JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.4DateUsing Similar TrianglesFor use with Activity 3.4Essential Question How can you use angles to tell whether triangles aresimilar?1ACTIVITY: Constructing Similar TrianglesUse a straightedge to draw a linesegment that is 4 centimeters long. Then use the line segment and aprotractor to draw a triangle thathas a 60o and a 40o angle as shown.Label the triangle ABC.80 90 10 070 10 0 90 80 110 170 2060 0 11060 132015 050 03160 170 180600 1 20 10 0150 3014 04 0 10180 170 1 20 36015 0 401 040Work with a partner.40 4 cma. Explain how to draw a larger triangle that has the same two anglemeasures. Label the triangle JKL.b. Explain how to draw a smaller triangle that has the same two anglemeasures. Label the triangle PQR.c. Are all of the triangles similar? Explain.Copyright Big Ideas Learning, LLCAll rights reserved.Big Ideas Math BlueRecord and Practice Journal63

Name Date3.42Using Similar Triangles (continued)ACTIVITY: Using Technology to Explore TrianglesWork with a partner. Use geometry software to drawthe triangle shown.Aa. Dilate the triangle by the following scale factors.21250 30 B14C2.5b. Measure the third angle in each triangle. What do you notice?c. REASONING When two angles in one triangle are congruent to two anglesin another triangle, can you conclude that the triangles are similar? Explain.3ACTIVITY: Indirect MeasurementWork with a partner.Fa. Use the fact that two raysfrom the Sun are parallelto explain why ABCand DEF are similar.x ftSun’s rayCSun’s ray5 ftA64Big Ideas Math BlueRecord and Practice Journal3 ftBD36 ftECopyright Big Ideas Learning, LLCAll rights reserved.

Name3.4DateUsing Similar Triangles (continued)b. Explain how to use similar triangles to find the height of the flagpole.What Is Your Answer?4. IN YOUR OWN WORDS How can you use angles to tell whether trianglesare similar?5. PROJECT Work with a partner or in a small group.a. Explain why the process in Activity 3 is called “indirect” measurement.b. CHOOSE TOOLS Use indirect measurement to measure the height ofsomething outside your school (a tree, a building, a flagpole). Beforegoing outside, decide what materials you need to take with you.c. MODELING Draw a diagram of the indirect measurement process youused. In the diagram, label the lengths that you actually measured andalso the lengths that you calculated.6. PRECISION Look back at Exercise 17 in Section 2.5. Explain how you canshow that the two triangles are similar.Copyright Big Ideas Learning, LLCAll rights reserved.Big Ideas Math BlueRecord and Practice Journal65

Name DatePractice3.4For use after Lesson 3.4Tell whether the triangles are similar. Explain.1.122 y 30 x 122 2.28 y x 40 86 52 3.y 65 105 40 4.x y 55 35 20 x 20 5. You can use similar triangles to find theAheight of a tree. Triangle ABC is similarto triangle DEC. What is the height ofthe tree?x ftD4 ftBE9 ft66Big Ideas Math BlueRecord and Practice JournalC6 ftCopyright Big Ideas Learning, LLCAll rights reserved.

lines to be parallel. Decide on a strategy for drawing two parallel lines. Then draw the two parallel lines. Draw a third line that intersects the two parallel lines. This line is called a transversal. a. How many angles are formed by the parallel lines and the transversal? Label

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