# Grecia Nava - Geo.Module2.Topic3.SE.pdf - TOPIC 3 Using...

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Lesson 1SSS, SAS, AAS, . . . S.O.S!Using Triangle Congruence to Determine Relationships Between Segments . . . M2-185Lesson 2Props To YouProperties of Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M2-197Lesson 3Three-Chord SongRelationships Between Chords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M2-225TOPIC 3Using Congruence Theorems© Carnegie Learning, Inc.Congruence theorems are all about analyzing triangles in terms of component sides and angles – especially right triangles.
TOPIC 3: Family Guide M2-183© Carnegie Learning, Inc.Carnegie Learning Family Guide GeometryModule 2: Establishing CongruenceTOPIC 3: USING CONGRUENCE THEOREMSAs students prove more theorems, they have a larger repertoire of reasons that they can use in new proofs. In this topic, students use the theorems that they have proved to prove new theorems about triangles, quadrilaterals, and angles formed in circles. Students use triangle congruence theorems to verify properties of parallelograms, and they use the congruence theorems they have proved to prove theorems related to the chords of circles. The fi nal lesson opens with a real-world scenario that students can think broadly about solving.Where have we been?Students build from the fundamentals of proof that they learned in the previous topic. Previously, students explained how the criteria for the SSS, SAS, and ASA congruence theorems follow from the definition of congruence in terms of rigid motion. And, students proved the AAS Congruence Theorem and the HA Congruence Theorem for right triangles. They now use these theorems to prove three additional congruence theorems for right triangles.Where are we going?Students will use logical reasoning not just in geometry but as they progress through advanced mathematics. Mathematics is about understanding and providing valid reasons why numeric, algebraic, and geometric relationships exist and whether or not they exist in all cases.Venn Diagram of QuadrilateralsThere have been different definitions of trapezoidover time. In this course, trapezoidis defined as “a quadrilateral with at least one pair of parallel sides.”QuadrilateralsKitesRhombiSquares RectanglesTrapezoidsParallelogramsIsoscelesTrapezoids
M2-184 TOPIC 3: Using Congruence Theorems© Carnegie Learning, Inc.Don’t Make a Mueller-Lyer Out of MeWhich of the blue lines shown is longer? Most people will answer that the line on the right appears to be longer. But in fact, both blue lines are the exact same length! This famous optical illusion is known as the Mueller-Lyer illusion. You can measure the lines to see for yourself. You can also draw some of your own to see how it almost always works! Appearances can be deceiving, which is why congruence in mathematics is defined precisely.Talking PointsIt can be helpful to know about geometric congruence for college admissions tests.