Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Theorems about similar triangles
Prove proportional-side and Pythagorean results using triangle similarity
Problem types
- Segments made by the altitude to the hypotenuse
- Lengths from similarity theorems
- Leg or altitude from the altitude to the hypotenuse
- Side lengths of a triangle cut by a parallel segment
- Perimeter of a triangle from a segment parallel to a side
- Choose the statement that is not always true for triangles made by parallel segments
- Show the work: the length that makes a segment parallel to a side
Builds on
- Proving triangles similar
- How a dilation changes a figure · Useful idea
A dilation keeps ratios of lengths, which makes corresponding sides of similar triangles proportional.
Leads to
- Sine and cosine of complementary angles · Extend the idea
The altitude to the hypotenuse makes two right triangles similar to the original, which shows the sine of one acute angle is the cosine of the other.
- Slopes of parallel and perpendicular lines · See it applied
Similar right triangles on two perpendicular lines show their slopes are negative reciprocals.
Related skills
- The Pythagorean theorem · Related idea
The two leg relations of a right triangle with its altitude add to give the Pythagorean theorem.
- Why every circle is similar to every other · Shared foundations
- Sine, cosine, and tangent · Shared foundations
Open the interactive map to explore lessons and skill connections.