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Learners connect right-triangle congruence ideas to general triangle congruence theorems (SSS, SAS, ASA, AAS), then define tangent segments and apply the Tangent Segment Theorem using measuring tools. Lesson structure spans construction, worked examples, proofs, and problem solving across two days.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/sss-sas-aas-using-triangle-congruence-to-determine-relationships-between-segments/386008/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/sss-sas-aas-using-triangle-congruence-to-determine-relationships-between-segments/386008.png","ImageObject",300,407,{"name":92,"@type":93},"Oliver","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-24",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the Hypotenuse-Leg Congruence Theorem used for in this lesson?","Question",{"text":112,"@type":113},"It establishes that if the hypotenuse and a leg of one right triangle are congruent to those of another right triangle, then the triangles are congruent. Students justify statements using a two-column proof and algebraic reasoning.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do Leg-Leg and Leg-Angle congruence relate to SSS, SAS, ASA, and AAS?",{"text":117,"@type":113},"The lesson explains that the Leg-Leg and Leg-Angle Congruence Theorems can be justified using SSS, SAS, ASA, and/or AAS triangle congruence. Students also describe the equivalence of these relationships for congruence cases.",{"name":119,"@type":110,"acceptedAnswer":120},"What are tangent segments and how is the Tangent Segment Theorem applied?",{"text":121,"@type":113},"Tangent segments are defined as tangents drawn from the same point on the exterior of a circle. 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They conclude that their various constructions result in a unique triangle. Students provide the reasons for statements in a two-column proof of the Hypotenuse-Leg Congruence Theorem and explain the algebraic reasoning used to justify this theorem. Students explain how the Leg-Leg Congruence Theorem and the Leg-Angle Congruence Theorem are equivalent to the SSS, SAS, ASA, or AAS Congruence Theorems. The term tangent segment is defined, and students use measuring tools to compare the lengths of tangent segments drawn from the same point on the exterior of a circle. The Tangent Segment Theorem is stated, and students analyze a Worked Example containing a proof plan for the theorem.  \nGeometry  \nLogical Argument and Constructions  \n(5) The student uses constructions to validate conjectures about geometric figures. The student is expected to:  \n(A) investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools.  \nProof and Congruence  \n(6) The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart. The student is expected to:  \n(B) prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions.  \nLESSON 1: SSS, SAS, AAS,   S.O. S! • 499A  \nCircles  \n(12) The student uses the process skills to understand geometric relationships and apply theorems and equations about circles. The student is expected to:  \n(A) apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems.  \nELPS  \n1.A, 1. D, 1. E, 2.C, 2. D, 2.G, 2. H, 2. I, 3.A, 3. B, 3.C, 3. D, 4.A, 4. B, 4.C, 4. K, 5. B, 5. E  \nEssential Ideas  \n• The Hypotenuse-Leg Congruence Theorem states: “If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.”  \n• The Leg-Leg Congruence Theorem states: “If the two corresponding shorter legs of two right triangles are congruent, then the triangles are congruent.”  \n• The Leg-Angle Congruence Theorem states: “If the leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another triangle, then the triangles are congruent.”  \n• The Leg-Leg and Leg-Angle Congruence Theorems can be justified using SSS, SAS, ASA, and/or AAS triangle congruence.  \n• The Tangent Segment Theorem states: “If two tangent segments are drawn from the same point on the exterior of a circle, then the tangent segments are congruent.”  \n499B • TOPIC 3: Using Congruence Theorems  \nLesson Structure and Pacing: 2 Days  \nDay 1  \nEngage  \nGetting Started: Pulling Your Leg  \nStudents construct a right triangle given line segments representing the length of a leg and the length of the hypotenuse. They use measuring tools to determine the measure of each angle and side, then compare these measurements to their classmates’ results. Students conclude that the given information determined a unique triangle.  \nDevelop  \nActivity 1.1: Hypotenuse-Leg Congruence Theorem  \nStudents provide the reasons for statements in a two-column proof of the Hypotenuse-Leg Congruence Theorem. Students explain the algebraic reasoning used to justify","cbCaiuUEaYhd2D1h","https://ap.wps.com/l/cbCaiuUEaYhd2D1h","pdf",1031253,"English","# Lesson Overview\n## Geometry: Logical Argument and Constructions\n## Proof and Congruence\n## Circles: Tangent Segments\n# Lesson Structure and Pacing: 2 Days\n## Day 1: Engage and Develop\n## Day 2: Tangent Segments and Demonstrate\n## Essential Ideas","[{\"question\":\"What is the Hypotenuse-Leg Congruence Theorem used for in this lesson?\",\"answer\":\"It establishes that if the hypotenuse and a leg of one right triangle are congruent to those of another right triangle, then the triangles are congruent. Students justify statements using a two-column proof and algebraic reasoning.\"},{\"question\":\"How do Leg-Leg and Leg-Angle congruence relate to SSS, SAS, ASA, and AAS?\",\"answer\":\"The lesson explains that the Leg-Leg and Leg-Angle Congruence Theorems can be justified using SSS, SAS, ASA, and/or AAS triangle congruence. Students also describe the equivalence of these relationships for congruence cases.\"},{\"question\":\"What are tangent segments and how is the Tangent Segment Theorem applied?\",\"answer\":\"Tangent segments are defined as tangents drawn from the same point on the exterior of a circle. Students use measuring tools to compare their lengths, then use the Tangent Segment Theorem and a worked example proof plan to solve problems.\"}]","SSS, SAS, AAS - Using Triangle Congruence to Determine Relationships Between Segments | PDF",1790271770]