In this topic, the student learns about various geometrical facts. In this series of five lessons, the student is introduced to the concept of congruence, learns about the volume and surface area of a cylinder, and finds missing angles in triangles and quadrilaterals.
This series furthers the geometrical knowledge the student possesses. The idea of two shapes being congruent gives the student another idea of similarity.
In this lesson, the student learns the idea of congruence. Multiple examples of congruence are shown, as well as multiple examples of shapes that appear alike that aren’t actually congruent.
This lesson teaches the student the formula for the volume of a cylinder. The lesson begins by reviewing the volume of rectangular prisms to show that volume is equal to the base area times the height. Then, the student is shown how the formula for the volume of a cylinder is derived from that basic premise.
This lesson introduces the student to the formula for the surface area of a cylinder. The lesson decomposes the cylinder into two circles and one rectangle to show the student that the surface area can be found by adding the areas of the circles to the area of the rectangle. The formula is then derived based on this idea.
In this lesson, the student learns that the sum of angles in triangles is one hundred eighty degrees while the sum of angles in quadrilaterals is three hundred sixty degrees.
This lesson builds upon the foundation of the previous lesson in order to show the student how they can find the unknown angle in a triangle or a quadrilateral. Since the student knows what the sum of the angles can be, the student can solve for the unknown angle. Examples show how this idea can be utilized in practice.