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ASA (angle-side-angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. The ASA postulate is attributed to Thales of Miletus. In most systems of axioms, the three criteria – SAS, SSS and ASA – are established as theorems.
The superior lumbar (Grynfeltt-Lesshaft) triangle is formed medially by the quadratus lumborum, laterally by the posterior border of internal abdominal oblique muscle, and superiorly by the 12th rib. The floor of the superior lumbar triangle is the transversalis fascia and its roof is the external abdominal oblique muscle.
With parallel lines, they are congruent. Alternate angles are the four pairs of angles that: have distinct vertex points, lie on opposite sides of the transversal and; both angles are interior or both angles are exterior. If the two angles of one pair are congruent (equal in measure), then the angles of each of the other pairs are also congruent.
Alternatively, the area can be calculated by dividing the kite into two congruent triangles and applying the SAS formula for their area. If a {\displaystyle a} and b {\displaystyle b} are the lengths of two sides of the kite, and θ {\displaystyle \theta } is the angle between, then the area is [ 27 ] A = a b ⋅ sin θ . {\displaystyle ...
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (Pythagoras' theorem). [6] [7] The law of cosines, a generalization of Pythagoras' theorem. There is no upper limit to the area of a triangle. (Wallis axiom) [8] The summit angles of the Saccheri quadrilateral are 90°.
The ratio of the area of the envelope of area bisectors to the area of the triangle is invariant for all triangles, and equals (), i.e. 0.019860... or less than 2%. A cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides.
Menelaus's theorem, case 1: line DEF passes inside triangle ABC. In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A ...
The femoral triangle is bounded: [2] superiorly (also known as the base) by the inguinal ligament. [2] medially by the medial border of the adductor longus muscle. (Some people consider the femoral triangle to be smaller hence the medial border being at the lateral border of the adductor longus muscle.) [2]