Module 5 Summary

1. Module 5 Summary

Mathematics 30-3 Module 5

Module 5 Summary

This is a photograph of a roof frame structure.

iStockphoto/Thinkstock

In this module you explored the properties of triangles, quadrilaterals, and regular polygons and how shapes can be transformed. You studied translations, rotations, reflections, and dilations on two- and three-dimensional shapes. You also learned about the sine law and the cosine law and how these laws can be used to solve problems involving triangles.

You worked to answer the module question: How can geometry be used in building and design?

In the Module 5 Project: Designing a Yard, you applied your knowledge of geometry to designing the yard of a home.

Some of the key points of this module are outlined in the following table.

triangles	Triangles can be classified based on length of sides as equilateral — all three sides are equal and all interior angles are equal isosceles — two sides are equal and two angles opposite equal sides are equal scalene — no sides are equal and no angles are equal Triangles can be classified based on size of angles as acute — all angles are less than 90° obtuse — one angle is greater than 90° right — one angle equals 90°
quadrilaterals	Quadrilaterals, or 4-sided polygons, can be classified based on length of sides, parallel sides, and measure of interior angles as a square rectangle trapezoid parallelogram rhombus Kite
regular polygons	Regular polygons have all sides equal in length and all interior angles equal in measure.
translations	Slide a shape left, right, up, or down.
rotations	A shape is turned to change its orientation.
reflections	A mirror image of the original shape is produced.
dilations	The size of the object is changed.
sine law	This law is used to determine an angle of a triangle that is not a right-angled triangle. This law is used to determine a side of a triangle that is not a right-angled triangle.
cosine law	This law is used to determine a side of a triangle that is not a right-angled triangle. This law is used to determine an angle of a triangle that is not a right-angled triangle.