6.1B Lesson: Building Triangles Given Three Measurements*

Transcription

1 6.1 Lesson: uilding Triangles Given Three Measurements* Name: Period: 1. ircle all the triangles with side lengths 8 and 5 and an included angle of 32. a. b. c. 2. ircle all the triangles with side lengths 4 and 3, with a non-included angle of 50 adjacent to the side with length 3. a. b. c. d. 3. ircle all the triangles with angles 90 and 28 and an included side of 6 units. a. b. c.

2 Term Definition Symbolic Name Example Included ngle of a Triangle The angle formed by two adjacent or neighboring sides of a triangle. Included Side of a Triangle The side formed by two angles that share a common segment (or ray) in a triangle. Discussion questions: What if you only have three pieces of information about a triangle, like two angle measurements and one side length? Is it possible to create more than one unique triangle with that information? sk the class as a whole and then have them write their response. Push them to start thinking about when they might get a unique triangle and when they might not. s students develop their conjectures, have them draw examples for the class. Station Rotation ctivity: re the triangles congruent? Materials: Protractors, rulers, and blank paper In this lesson the class rotates through six stations. For a large class you can have two simultaneous rotations. t tables One through Five, students are discovering what criteria works to form congruent triangles. Students will need blank paper, or the back of module pages, to do the station rotation. Table six can be a reteach or discussion station, in which the teacher will meet with every group by the end of the lesson. t the end of the rotations, the class should have a group discussion to review which combinations are valid to prove triangles congruent. Table 1 will require that students use 3 rulers or protractors as a group until they are able to get all sides with the correct measurement. ompasses are not needed for this.

3 Station Instruction ards: TLE 1 Each person needs to draw an equilateral triangle that has each side equal to 4 inches in length. 1. If all the people in your group drew congruent triangles, is it possible to draw a triangle that fits TLE 2 Each person needs to draw a triangle that has two sides that measure 4 inches in length, with an included angle measuring 80 degrees. TLE 3 Each person needs to draw a triangle that has a side length 4 inches and another side length 3.25 inches. One non-included angle needs to be equal to 50 degrees. TLE 4 Each person needs to draw a triangle that has angles with the following measures: 30 degrees, 100 degrees, and 50 degrees. TLE 5 Each person needs to draw a triangle that has one side equal to 4 inches, and the two angles coming off that side to measure 30 degrees and 50 degrees.

4 In the two triangles below, measure each side to the nearest tenth of a centimeter, and measure each angle to the nearest degree. Record your results D E F = 3.4cm EF = 2.4cm = 5.1cm DF = 4.7cm = 6.1cm DE = 6.2cm 6. Use a ruler to draw scalene, such that is the longest side and is the shortest side. Measure each side to the nearest tenth of a centimeter, and measure each angle to the nearest degree. ZY = XZ = XY = 7. Describe the relationship between the location of the longest side and the location of the largest angle of the three triangles in #4-6 above,,, and. The longest side is opposite, or across from, the largest angle for all three triangles. 8. Describe the relationship between the location of the shortest side and the location of the smallest angle of the three triangles above. The shortest side is opposite, or across from, the smallest angle for all three triangles.

5 Summarize The Findings: If two sides in a triangle are not congruent, then the angles opposite those sides are also not congruent, and the larger angle is opposite the longer side and the smallest angle is opposite the shortest side. In the following triangles, fill in the missing angle measurements and list the sides of the triangle from shortest to longest without using a ruler. Teacher Note: Discuss with students that pictures are not necessarily to scale. 9.,, 10.,, 11.,, In the following triangles, list the angles of the triangle from smallest to largest without using a protractor. Teacher Note: Discuss with students that pictures are not necessarily to scale