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Discovering Similarity Postulate Through Triangle Construction and Theorems

In this activity, students will discover the similarity of triangles by constructing two triangles, ABC and DEF, with given angle measures. By applying the Angle-Angle (AA) Similarity Postulate, students will learn that triangles are similar if their corresponding angles are congruent. Additionally, they will explore the Side-Side-Side (SSS) and Side-Angle-Side (SAS) Similarity Theorems, which provide criteria for triangle similarity based on the proportionality of their corresponding sides. This hands-on approach reinforces understanding of geometric concepts.

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Discovering Similarity Postulate Through Triangle Construction and Theorems

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  1. 7.3 Activity: Discovering A Similarity Postulate • Draw triangle ABC with m<A = 60 and m<B = 40 • Draw another triangle DEF with m<D =60 and m<E = 40, and DE > AB. • Copy and complete the chart below:

  2. Warm-up • How many of your brackets are busted? Today Warm-up Discuss quiz Objective Guided notes Example problems “Have more than you show, speak less than you know.” –William Shakespeare, King Lear

  3. Chapter 7 7.3-7.4 Similar Polygons Obj: _______________________ ____________________________

  4. Angle-Angle (AA) Similarity Postulate • If the angles of one triangle are congruent to the angles of a second triangle, then the triangles are similar. If <K = <Y and <J = <X Then, KLJ ~ YZX K Y X Z J L

  5. USING SIMILARITY THEOREMS THEOREMS P A AB PQ BC QR CA RP Q R If = = B C THEOREM 8.2 Side-Side-Side (SSS) Similarity Theorem If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. then ABC ~ PQR.

  6. Warm-up • Have your notes out and ready to go. • Grades are up to date on HAC make sure you have everything turned in. Today Warm-up Guided notes Homework problems “Have more than you show, speak less than you know.” –William Shakespeare, King Lear

  7. USING SIMILARITY THEOREMS THEOREMS X M P N Z Y XY MN ZX PM If XM and= THEOREM 8.3 Side-Angle-Side (SAS) Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. then XYZ ~ MNP.

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