Triangle Proportionality Theorem
The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divides those two sides proportionally. In other words, if a line is parallel to one side of a triangle, it creates a proportion with the lengths of the sides that it intersects.
Triangle Proportionality Theorem Proof
The proof of the Triangle Proportionality Theorem involves showing that corresponding sides of the triangles formed by the parallel line are in proportion.
Triangle Proportionality Theorem Formula
The formula for the Triangle Proportionality Theorem can be expressed as follows:
If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally.
Triangle Proportionality Theorem Calculator
A calculator can be used to determine the proportional divisions of the sides when a line is parallel to one side of a triangle.
Converse of the Triangle Proportionality Theorem
The Converse of the Triangle Proportionality Theorem states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side.
The Side-Angle-Side (SAS) Similarity Theorem states that if an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.
SAS Similarity Theorem Proof
The proof of the SAS Similarity Theorem involves showing that the corresponding angles of the triangles are congruent and the corresponding sides are in proportion.
A similarity transformation involves a dilation, which is a transformation that produces an image that is the same shape as the original, but is a different size.
Similarity Transformation and Dilation Formula Worksheet
A worksheet can be used to practice applying the formula for similarity transformation and dilation.
Similarity Transformation and Dilation Formula PDF
For further study, a PDF document can provide examples and explanations of similarity transformation and dilation.
Examples of Similarity Transformation
Understanding how to apply the similarity transformation and dilation formula can be achieved through working through examples that demonstrate the process.
Formula for Dilation Not at Origin
The formula for dilation not at the origin involves scaling the coordinates of the original figure.
Perform Similarity Transformation
Performing a similarity transformation involves applying the formula for dilation and determining whether a figure has been reduced or enlarged based on the scale factor.
By understanding and applying the theorems of triangles and the formulas for similarity transformation and dilation, students can gain a deeper understanding of geometric relationships and proportions within triangles.
