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Geometry: Similarity, Right Triangles, and Trigonometry

458 questions21 skills


42 questions3 skills
Verify experimentally the properties of dilations given by a center and a scale factor:


12 questions1 skill
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.


42 questions3 skills
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.


44 questions3 skills
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Skills for this standard are coming soon.
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
Skills for this standard are coming soon.


18 questions1 skill
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Explain and use the relationship between the sine and cosine of complementary angles.
Skills for this standard are coming soon.
Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
Skills for this standard are coming soon.


85 questions3 skills
Prove the Laws of Sines and Cosines and use them to solve problems.


85 questions3 skills
Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.