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1 Lesson Plan #18 Date: Wednesday October 21st, 2015 Class: Geometry Topic: Proving triangles congruent by the S.A.S postulate HW #18: Read pages 117-118, page 120 #’s 1, 4, 7, 10 Page 123 #’s 1-3 Aim: How do we prove triangles congruent by the S.A.S postulate? Note: Give scrap paper to students. Objectives: 1) Students will be able to define congruent polygons. 2) Students will be able to define corresponding parts of congruent polygons 3) Students will be able to understand the S.A.S. postulate. 4) Students will be able to use the S.A.S. postulate to prove triangles congruent. F A E B J G C D H I Do Now: At right are two polygons (what type? _____________) where one can be moved in such a way that the sides and angles of one polygon fit exactly upon the sides and angles of the second polygon. How do we classify these two polygons? PROCEDURE: Write the Aim and Do Now Get students working! Take attendance Give Back HW Collect HW Go over the Do Now In geometry, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. http://www.mathsisfun.com/geometry/congruent.html http://www.mathopenref.com/congruentpolygons.html In the congruent polygons, what vertex in the 2nd polygon corresponds to vertex A in the first polygon? Name the other corresponding vertices Name the corresponding sides Definition: Two polygons are congruent if their vertices can be matched up so that the corresponding sides and angles (or corresponding parts for short) of the polygons are congruent. Online Activity: Let’s mark the corresponding parts in the congruent triangles below. Indicate the corresponding parts of the congruent triangles at right Online activity: http://www.mathopenref.com/congruenttriangles.html Examine the two triangles at left with the indicated sides and angles congruent. What do you notice about the two triangles? Let’s explore pairs of triangles that have two corresponding sides congruent and the included angle congruent http://www.mathopenref.com/congruentsas.html 2 Postulate: Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other [s.a.s.] [s.a.s.] Online Activity: http://www.glencoe.com/sites/texas/student/mathematics/assets/animation/geometry/GEOCIM4-4.swf Follow along with a piece of scrap paper. Assignment #1: How many different (size) triangles can you construct using the two sides and the included angle below? Assignment #2: 3 Example #1: Statements Reasons Example #2: Statements Reasons On Your Own: Complete the 3 proofs below: Do the proofs on a separate sheet of graph paper. 14. Determine if the pair of triangles are congruent. If they are, state the rigid motions that would justify the triangles being congruent. Then state the congruence postulate that would show the triangles are congruent. Rigid Motion: Congruence Postulate: Final Summary: Side Angle Side - (SAS) If there is a correspondence between two sides and the included angle of two triangles, such that corresponding sides are congruent and the corresponding included angles are congruent, then the triangles must be congruent. 4 If Enough Time: Statements Reasons Statements Reasons Statements Reasons Statements Reasons