What is the altitude theorem?

What is the altitude theorem?

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of the two segments equals the altitude.

What is converse Pythagorean Theorem?

The converse of the Pythagorean Theorem is: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

What is hypotenuse leg theorem?

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

What kind of triangle is 30 60 90?

special right triangle
The 30-60-90 triangle is called a special right triangle as the angles of this triangle are in a unique ratio of 1:2:3. Here, a right triangle means being any triangle that contains a 90° angle.

How do you prove converse of the BPT Theorem?

1. Statement : If a line divide any two sides of a triangle (Δ) in the same ration, then the line must be parallel (||) to third side.
2. Given in ΔABC, D and E are two points of AB and AC respectively, such that,
3. Let us assume that in ΔABC, the point F is an intersect on the side AC.

How do you find the hypotenuse leg theorem?

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides (base and perpendicular). This is represented as: Hypotenuse² = Base² + Perpendicular².

What is Pappus’ theorem?

T oday we will learn about Pappus’ theorem. This theorem states that if we take three points , , on a line, and another three points , , on another line, then the three intersection points of the following line pairs are collinear. P appus’ theorem looks very similar to Pascal’s hexagon theorem.

What is the Pappus configuration of the Cayley–Bacharach theorem?

Pascal’s theorem is in turn a special case of the Cayley–Bacharach theorem . The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus’s theorem, with each line meeting 3 of the points and each point meeting 3 lines.

What is the Pappus configuration in geometry?

The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus’s theorem, with each line meeting 3 of the points and each point meeting 3 lines. In general, the Pappus line does not pass through the point of intersection of ABC and abc.

What is the name of the hexagon of the Pappus line?

The hexagon is AbCaBc. In mathematics, Pappus’s hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear, lying on the Pappus line.