Students will be able to apply the Intersecting Chords Theorem to find the lengths of segments created by chords intersecting inside a circle.
Students will demonstrate their understanding by solving problems involving segments from chords within circles.
Chords: Segments that connect two points on a circle.
Segments within a Circle: Portions of a circle divided by chords.
Intersecting Chords Theorem: If two chords intersect within a circle, the product of the segments of one chord is equal to the product of the segments of the other chord. This can be represented by the formula: AB * BC = CD * DE, where AB and BC are segments of one chord and CD and DE are segments of the other chord.
Engage students by displaying a diagram of a circle with intersecting chords and asking: "How can we determine the length of segments created by these chords?"
Define chords and segments within a circle
Explain the Intersecting Chords Theorem and its application
Anticipated misconception: Students may confuse the lengths of segments and chords within a circle.
Provide examples of intersecting chords for students to work through
Scaffold questioning from basic calculations to more complex problem-solving
Monitor student progress by circulating the room and providing guidance as needed
Assign a series of problems involving segments from chords
Ensure students show their work clearly to demonstrate understanding
Provide additional support for students who may need it
Have students share their responses to the opening question to summarize the key learning points of the lesson.
Early finishers can explore real-world applications of segment lengths within circles, such as in architecture or design.
Homework activity suggestion: Create a set of circle diagrams with intersecting chords and ask students to calculate segment lengths based on the given information.
CCSS.MATH.CONTENT.HSG-C.A.4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.
CCSS.MATH.CONTENT.HSG-C.A.4b: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.