Unit 3: Triangles, Congruence, and Other Relationships
In this unit, we will explore different methods for comparing and identifying identical triangles depending on the information we have available. Whether we compare pieces of furniture, automobiles, or pieces of a candy bar, we will have to make sure that objects are the same size and shape.
We will also study triangles and their parts to predict their measurements and distances between them. For example, we can use the process of triangulation to calculate a distance when we have two known locations. This can be useful when we need to calculate precise measurements for a land survey on a building construction site, determine distances for a race, or calculate the correct angles for a rocket launch.
Completing this unit should take you approximately 5 hours.
3.1: Triangle Classification
Before we can begin comparing triangles, we need to be able to classify triangles based on their angles and sides.
3.2: Triangle Sum Theorem
The triangle sum theorem states that the sum of the interior angles in a triangle add to 180 degrees. This theorem is useful when we need to solve for an unknown angle in a given triangle.
3.3: Exterior Angle Theorem
The exterior angle theorem states that an exterior angle of a triangle equals the sum of its nonadjacent interior angles. Like the triangle sum theorem, it allows us to determine unknown angles in a given triangle.
3.4: Congruent Figures
Congruent figures are figures that are exactly the same shape and size.
3.5: Congruent Triangles and SSS
We can use the side-side-side (SSS) postulate for triangles to determine whether triangles are congruent. The SSS postulate states that if the three sides of two triangles are congruent, then the triangles are congruent.
3.6: Other Triangle Congruence Postulates
While the SSS postulate is useful, sometimes we do not have enough information about the sides of two triangles to use it. We can use other postulates depending on the given information for a pair of triangles. These additional postulates include side-angle-side (SAS), angle-side-angle (ASA), and angle-angle-side (AAS).
3.7: Calculating Congruent Triangles
Now that we have explored the different ways to determine whether two triangles are congruent, we will use what we learned to solve congruence problems.
3.8: Isosceles Triangles
Isosceles triangles are triangles that have at least two congruent sides.
3.9: Equilateral Triangles
Equilateral triangles are the last special type of triangle we explore in this unit. In an equilateral triangle, all sides and angles are congruent.