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\n\n20\nItems in Unit\n\n
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\n\"Geometry\n\n
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\nLesson Planet Curated\n
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\nGeometry Unit 2: Reasoning and Proof\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nThe four lessons in the Geometry Unit 2 module are all about reasoning and proof. In the first lesson pupils watch a video introducing conditional statements and their related statements. Learners find out how to identify the hypothesis...\n
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\n\n35\nItems in Unit\n\n
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\n\"Geometry\n\n
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\nLesson Planet Curated\n
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\nGeometry Unit 3: Parallel and Perpendicular Lines\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nThe Geometry Unit 3: Parallel and Perpendicular Lines Unit Module contains seven lessons, each with a video, teacher reference, practice packets and solutions, and corrective assignments. In the first lesson, pupils learn eight...\n
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\n\n10\nItems in Topic\n\n
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\n\"Mathematics\n\n
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\nLesson Planet Curated\n
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\nMathematics Vision Project: Interactive Applets\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nReady, set, go! The Mathematics Vision Project provides a collection of 10 Interactive Applets that follow the progression of learning—to practice, develop, and solidify understanding. The interactives use engaging materials that include...\n
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\n\n12\nItems in Course\n\n
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\n\"Flipped\n\n
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\nLesson Planet Curated\n
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\nFlipped Math: Geometry\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nImagine taking a complete geometry course remotely! Eleven units make up the My Geometry course. Each unit follows the Flipped-Mastery cycle of learning, divided into two semesters. Pupils watch and take notes on a video that details the...\n
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\n\n37\nItems in Unit\n\n
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\n\"Geometry\n\n
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\nLesson Planet Curated\n
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\nGeometry Unit 5: Quadrilaterals and Polygons\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nOne's knowledge of angles should measure up to expectations. Scholars watch a video to learn about angles in polygons. They first see how to partition a polygon into triangles to find the sum of the interior angle measures. They then...\n
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Instructional Video2:56
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\n\"Parallel\n\n
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\nCK-12 Foundation\n
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\nParallel Lines and Transversals: Lesson\n

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\n\nFor Students\n\n7th - 11th\n\nStandards\n
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\nSegment transversals proportionally. Given a diagram with three parallel lines and two transversals, the narrator of a short video points out the parallel lines cut the transversals proportionally. The portion of a long playlist on...\n
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Unit Plan
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\n\"Parallel\n\n
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\nRadford University\n
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\nParallel Lines Cut by a Transversal\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nUse the parallel lines to find your way. After first reviewing geometric constructions and the relationships between angles formed by parallel lines and a transversal, young mathematicians write proofs for theorems relating to parallel...\n
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Instructional Video3:48
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\n\"Parallel\n\n
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\nKhan Academy\n
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\nParallel Lines From Equation, Mathematics I, High School Math\n

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\n\nFor Students\n\n7th - 9th\n
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\nHere is a fairly basic video that uses three equations, each written in slope-intercept form, to determine whether the lines are parallel. Sal graphs each equation on the same coordinate plane to show how their slopes compare. The video...\n
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Lesson Plan
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\n\"Looking\n\n
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\nEngageNY\n
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\nLooking More Carefully at Parallel Lines\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nCan you prove it? Making assumptions in geometry is commonplace. This resource requires mathematicians to prove the parallel line postulate through constructions. Learners construct parallel lines with a 180-degree rotation and then...\n
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Lesson Plan
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\n\"Characteristics\n\n
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\nEngageNY\n
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\nCharacteristics of Parallel Lines\n

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\n\nFor Teachers\n\n8th\n\nStandards\n
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\nSystems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...\n
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Unit Plan
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\n\"Parallel\n\n
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\nRadford University\n
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\nParallel Lines, Transversals, and Angles: What’s the Connection?\n

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\n\nFor Students\n\n9th - 11th\n\nStandards\n
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\nStreets, bridges, and intersections, oh my! Parallel lines and transversals are a present in the world around us. Learners begin by discovering the relationship of the angles formed by parallel lines and a transversal. They then...\n
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Unit Plan
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\n\"Parallel\n\n
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\nRadford University\n
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\nParallel Lines Cut By a Transversal\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nPerhaps planning a city isn't so difficult after all. Scholars first perform geometric constructions and investigate how parallel lines are useful in real-world situations. They then work on a city design project, drawing street maps,...\n
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Instructional Video16:33
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\n\"More\n\n
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\nFlipped Math\n
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\nMore with Proofs\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nProofs may be as easy as 1, 2, 3 ... maybe. Pupils participate in creating four example proofs. The presentation uses a list of geometric properties to develop the proofs by filling in both the statements and reasons. Scholars practice...\n
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Lesson Plan
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\n\"Informal\n\n
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\nEngageNY\n
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\nInformal Proofs of Properties of Dilations\n

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\n\nFor Teachers\n\n8th\n\nStandards\n
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\nChallenge the class to prove that the dilation properties always hold. The lesson plan develops an informal proof of the properties of dilations through a discussion. Two of the proofs are verified with each class member performing the...\n
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Interactive
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1
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\n\"Conjectures\n\n
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\nGeoGebra\n
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\nConjectures and Proof\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nTransform proofs using triangle rotations. By rotating a triangle around various points, class members develop proofs. Participants prove relationships of alternative interior angles formed by parallel lines and the sum of the interior...\n
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Instructional Video9:49
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\n\"Proof:\n\n
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\nKhan Academy\n
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\nProof: sin(a+b)=(cos a)(sin b)+(sin a)(cos b)\n

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\n\nFor Students\n\n10th - 12th\n
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\nSal proves the sum of angles formula for sine, sin (a+ b) = cos (a) sin (b) + sin (a) cos (b), through a clear but rather non-intuitive proof. The proof is interesting as it uses the SOH-CAH-TOA model and requires one to recall some...\n
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Lesson Plan
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\n\"Unknown\n\n
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\nEngageNY\n
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\nUnknown Angle Proofs—Proofs of Known Facts\n

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\n\nFor Teachers\n\n9th - 10th\n\nStandards\n
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\nLead the class in a Greek history lesson with a geometric twist. Pupils relate a short video about geometric properties to modern-day methods of solving for unknown angles. They discuss parallel line theorems and complete...\n
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Lesson Plan
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\n\"Determining\n\n
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\nCurated OER\n
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\nDetermining Angle Measure with Parallel Lines\n

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\n\nFor Teachers\n\n9th - 12th\n
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\nStudents observe and solve examples of corresponding angle postulates, alternate interior angle theorems, and exterior and consecutive angles. They complete the Determining Angle Measure With Parallel Lines worksheet.\n
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Instructional Video9:22
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\n\"Proof:\n\n
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\nKhan Academy\n
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\nProof: cos(a+b)=(cos a)(cos b)-(sin a)(sin b)\n

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\n\nFor Students\n\n10th - 12th\n
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\nUsing a similar method that he used to prove the sum of angles formula for sine, Sal shows the proof of the cosine sum of angles formula, cos (a+ b) = cos (a) cos (b) - sin (a) sin (b). This proof also uses the SOH-CAH-TOA model and some...\n
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Instructional Video9:36
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\n\"Proving\n\n
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\nProving Lines Parallel\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nShow it can all be proved. Scholars learn the converses of the properties of parallel lines. Using the converses, pupils determine which lines are parallel based on angle measurements and practice using a flow proof to show that two...\n
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Worksheet
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\n\"Accelerated\n\n
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\nGeometry Accelerated\n
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\nAccelerated Geometry Review Sheet\n

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\n\nFor Students\n\n8th - 10th\n\nStandards\n
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\nYour geometry learners use their knowledge of various geometric concepts to write proofs. Starting with givens containing parallel line segments with transversals and triangles and quadrilaterals, and the mid-point and distance formulas;...\n
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Instructional Video14:37
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\n\"Parallel\n\n
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\nParallel Lines and Triangles\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nTriangles bring sums to geometry. The lesson presents two theorems dealing with the angles of a triangle. Pupils learn about the Triangle Sum Theorem and the Exterior Angle Theorem, and then apply the theorems to create equations and...\n
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Worksheet
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\n\"Parallel\n\n
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\nCurated OER\n
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\nParallel Lines\n

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\n\nFor Students\n\n10th\n
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\nIn this parallel lines worksheet, 10th graders solve and complete 16 different types of problems. First, they name the lines that are parallel to those listed. Then, students find that values that make each set of line parallel. They...\n
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Unit Plan
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\n\"Congruence,\n\n
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\nCongruence, Proof, and Constructions\n

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\n\nFor Teachers\n\n8th - 10th\n\nStandards\n
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\nThis amazingly extensive unit covers a wealth of geometric ground, ranging from constructions to angle properties, triangle theorems, rigid transformations, and fundamentals of formal proofs.  Each of the almost-forty lessons...\n
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