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CONGRUENCE MS. SPRADLIN GEOMETRY 2016-17 INTRODUCTION • Today, we will move on to the topic of triangles, but this chapter will be all about determining if two triangles are the same or what mathematicians like to say, congruent. I found a video on YouTube which introduces most of the topics we will be covering in this chapter. While you are listening, write down some of the topics that are mentioned. Keep this sheet and refer back to it throughout the chapter. By the end, you should be able to explain almost everything that you wrote down. VIDEOS • https://www.youtube.com/watch?v=_L8u8io6n2A&feature=related • https://www.youtube.com/watch?v=kSV5Plfbq48&spfreload=10 WHAT TOPICS CAN YOU REMEMBER FROM THE VIDEOS? • SAS • SSS • ASA • AAS • HL • CPCTC • Congruence • Corresponding TODAY • We will be discovering the usefulness of congruence and corresponding parts • There are specific notations to show congruence • Congruent • Angle - ≅ - SAME ∠ • Triangle • Congruent sides on a triangle • Write the letters of the triangles clockwise starting with the lowerleft corner and wrapping around the triangle DEFINITIONS • Congruence - Exactly equal in size and shape. Congruent sides or segments have the exact same length. Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent. • Corresponding parts - Corresponding parts in a figure mean that the parts (angles or sides) are in the same relative position in each of the figures. HOW TO DEPICT CONGRUENT TRIANGLES • There are specific notations to show congruence. YOU WILL NEED TO WRITE CONGRUENCE STATEMENTS When two triangles are congruent, there are 6 facts that are true about the triangles: the triangles have 3 sets of congruent (of equal length) sides and the triangles have 3 sets of congruent (of equal measure) angles. NOTE: The corresponding congruent sides are marked with small straight line segments called hash marks. The corresponding congruent angles are marked with arcs. IT IS TIME FOR YOU TO TRY • You will be shown two triangles and they should shout out if you think that the triangles are congruent to not congruent. ARE THEY CONGRUENT OR NOT CONGRUENT? Congruent Congruent Non-congruent DANCING ACTIVITY • Wander around the room during the music: https://www.youtube.com/watch?v=zq7Eki5EZ8o • When the music stops go up to the student closest to you and determine whether or not your triangles are congruent • Go to the appropriate side of the classroom – I will check you for accuracy • You will be asked to identify the parts that keep the triangles from being congruent • We will do this three times! On the third time, you will switch triangles with someone before we dance! NEXT!!! • Time to do some examples!!! R EXAMPLE Y Q ? 10 95 • Find the length of line XZ, and find the measure of angle Q • Can you find the corresponding angles? P X Z ? REVIEW • Congruence - Exactly equal in size and shape. Congruent sides or segments have the exact same length. Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent. • Corresponding parts - Corresponding parts in a figure mean that the parts (angles or sides) are in the same relative position in each of the figures. CLOSURE • You are to write a paragraph discussing what you have learned. The structure should start with a thesis statement, include supporting sentences relevant to the thesis statement, and should end with a statement that summarizes what was said. • You will be graded on accuracy, grammar, and paragraph structure (Gardner’s: Linguistic) • You will also have homework problems which you can work on if you get done early, which will be due the next tomorrow.