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Working in pairs, geometry students will construct a dilation and consider the properties associated with the similar figures that are created to verify the properties of dilation. This activity can be done using dot or graph paper and rulers, compasses, and protractors, geoboards, or dynamic geometry software. Extensions can be added by considering dilations affected by different scale factors, or by dilating other figures such as triangles or parallelograms.
Most high schoolers are very familiar with the area of the triangle being equal to 1/2 base times the height. Here, they will develop and test their formula for the area of a triangle when given two adjacent sides and the included angle. After they develop their formula, they will use a dynamic geometry software system, such as Geometer's Sketchpad or GeoGebra to test their conjecture.
The University of New York Regents High School Exam for geometry from August 2009 is comprehensive in scope with 38 questions over 22 pages. Geometers can assess their mastery of core content with a combination of multiple choice and constructed response questions. A reference sheet with relevant formulas is included.
Learners explore the concept of geometry. In this geometry lesson plan, students practice problems from the geometry regents exam. Learners answer practice problems that are multiple choice. Students answer questions involving angle measures, parallel lines, shapes, congruent figures, circles, perpendicular lines, etc.
Students examine basic geometry terms and attempt to discover why geometry was developed and how we use geometry in our everyday life. In this using Geometers Sketchpad lesson, students explore a variety of activities pertaining to geometric knowledge. Students then complete a group assessment and complete an individual essay test.
Young scholars practice the high school Regents exam. In this high school regents exam lesson, students practice geometry sample problems from a past Regents exam. Young scholars solve problems involving angle measures, side lengths, parallel and perpendicular lines, Pythagorean theorem, and other geometry topics.
Students explore the concept of geometric history. In this geometric history lesson, students find lunes using a graphing calculator. Students use their knowledge of perpendicular bisectors, medians, and altitudes to construct lunes. Students construct the Euler line, nine point circle, and Simson line.
Tenth graders explore the Euler Line. In this geometry lesson, 10th graders use Cabri Jr. to construct the circumcenter, incenter, orthocenter, and centroid of a triangle. Students examine the four points and construct a line, the Euler line, that passes through three of the four points. Students determine which point should be excluded and examine the conditions under which all four points would lie on the line.
Here is a clever, cross-curricular lesson that combines art and geometry. Learners design a painting that uses geometrical shapes and is symmetrical. Sponge-shaped geometrical figures are used to design half a page and fold them to create the other half. Everyone displays their pictures of geometry and symmetry.
Middle schoolers identify the correspondence between pairs of angles. They fill in the blank for seven questions. Learners investigate congruency using their graphing calculator and by following detailed directions. They identify alternate exterior angles on their graphing calculator. There are seven calculator problems and four questions about a pair of parallel lines cut by a transversal.