Triangles
A triangle is a polygon with three sides and three angles. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the measure of their angles.
Types of Triangles based on Sides:
- Equilateral Triangle: A triangle with all three sides of equal length.
- Isosceles Triangle: A triangle with at least two sides of equal length.
- Scalene Triangle: A triangle with no sides of equal length.
Types of Triangles based on Angles:
- Acute Triangle: A triangle with all three angles less than 90 degrees.
- Right Triangle: A triangle with one right angle (90 degrees).
- Obtuse Triangle: A triangle with one angle greater than 90 degrees.
Properties of Triangles:
- The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- The longest side of a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.
- The area of a triangle can be calculated using the formula: A = (1/2) * base * height
Pythagorean Theorem:
In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem: a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Study Guide:
- Learn the properties of different types of triangles, including their angles and side lengths.
- Practice identifying and classifying triangles based on their properties.
- Understand the Pythagorean theorem and how it applies to right-angled triangles.
- Solve problems involving the area of triangles using the formula A = (1/2) * base * height.
- Practice using the triangle inequality theorem to determine if a set of side lengths can form a triangle.
◂Math Worksheets and Study Guides Fifth Grade. Positive & Negative Integers
Study Guide
Positive & Negative Integers 
Worksheet/Answer key
Positive & Negative Integers Worksheet/Answer key
Positive & Negative Integers Worksheet/Answer key
Positive & Negative Integers Worksheet/Answer key
Positive & Negative Integers
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Number and Operations (NCTM)
Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Explore numbers less than 0 by extending the number line and through familiar applications.
Algebra (NCTM)
Use mathematical models to represent and understand quantitative relationships.
Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
Connections to the Grade 5 Focal Points (NCTM)
Number and Operations: Building on their work in grade 4, students extend their understanding of place value to numbers through millions and millionths in various contexts. They apply what they know about multiplication of whole numbers to larger numbers. Students also explore contexts that they can describe with negative numbers (e.g., situations of owing money or measuring elevations above and below sea level).