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Good Morning!

This lesson focuses on proving triangles congruent using a coordinate proof. Students will plot points on a coordinate grid, find lengths using the distance formula, and explore shortcuts for proving congruence. The lesson includes hands-on activities using rulers, protractors, and pencils.

mhampton
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Good Morning!

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Presentation Transcript

  1. Good Morning! Please take out your homework from last night and your 4.4 review worksheet and clear off your desks.

  2. Objective: Prove triangles are congruent using a coordinate proof. Triangle ABC has points A(-3, 1), B(-5, -4), and C(-2, -5). Triangle PQR has points P(4, 7), Q(2, 2), and R(5, 1). Prove ∆ABC ≅ ∆PQR First: Plot the points on a coordinate grid.

  3. Now find the length of AB, AC, BC, PQ, QR, and PR using the distance formula.

  4. Do you think architects have to measure all 3 angles and all 3 sides in one triangle to make sure it is congruent to another triangle? Or are there shortcuts?

  5. In Lesson 4-4, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent.

  6. Materials:You should each have a ruler, popsicle stick, and protractor, and pencil. Use your pencil, popsicle stick, and ruler to create a triangle. Can you and your team members create two different triangles given equal side lengths? Or do your triangles always end up being exactly the same shape and size. Remember: Just because your triangles are in a different orientation, does not mean they aren’t congruent.

  7. First shortcut: SSS You only need to know that two triangles have three pairs of congruent corresponding sides. This can be expressed as the following postulate.

  8. To create this play dome, the directions don’t specify angle measures because if all the stick pieces are congruent, the triangles are automatically congruent. There is only one possible triangle you can make.

  9. Let’s check if SAS works. An included angle is an angle formed by two adjacent sides of a polygon. B is the included angle between sides AB and BC.

  10. http://www.geogebratube.org/student/m5253 • Materials: Ruler, sharpened pencil, protractor, sheet of paper. • Procedure: Measure a line segment that is 6 inches long. • Create a 65 degree angle with the line. • Make the other ray 7 inches long. • Is there only one possible triangle you can make?

  11. Let’s check if AAA works? • If three angles in one triangle correspond to three angles in another triangle, are the triangles automatically congruent? • Why or why not? http://tube.geogebra.org/student/m26172

  12. Quick Check Which postulate, if any, can be used to prove the triangles congruent? 1. 2. 3. 4.

  13. Objectives Apply SSS and SAS to construct triangles and solve problems. Prove triangles congruent by using SSS and SAS.

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