What is the hinge theorem in geometry?
Geometry. The Hinge Theorem states that if two sides of two triangles are congruent and the included angle is different, then the angle that is larger is opposite the longer side.
What theorem states that if two angles of a triangle are not congruent then the longer side lies opposite the larger angle?
Converse of the Hinge Theorem (SSS Inequality) If two sides of one triangle are congruent to two sides of another triangle and the third sides are not congruent, then the larger included angle is opposite the larger third side.
How do you prove the circumcenter?
Circumcenter Proof
- The circumcenter is equidistant from the three vertices of the triangle.
- 1) Triangle ABC; Perpendicular bisectors of each side(Given)
- 2) DA = DB, DC = DB(If a point is on the perp.
- 3) DA = DB(Substitution)\
- 4) D is on the perpendicular bisector of seg.
Is there an orthocenter theorem?
Theorem: Orthocenter Theorem The three altitudes from the vertices to the opposite sides of a triangle are concurrent.
What is Hinge Theorem example?
The Hinge Theorem states that in the triangle where the included angle is larger, the side opposite this angle will be larger. It is also sometimes called the “Alligator Theorem” because you can think of the sides as the (fixed length) jaws of an alligator- the wider it opens its mouth, the bigger the prey it can fit.
What is the formula of Hinge Theorem?
The theorem states the following: If two sides of one triangle are congruent, respectively, to two sides of a second triangle, and the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second.
What is the relationship of ∠ 1 and ∠ 2?
∠1 and ∠2 are supplementary. 90 + m∠2 = 180 Substitute 90 for m∠1. m∠2 = 90 Subtract 90 from each side.
What is the median theorem?
The Median Theorem states that the medians of a triangle intersect at a point called the centroid that is two-thirds of the distance from the vertices to the midpoint of the opposite sides.
What is Orthocentre formula?
There is no direct formula to calculate the orthocenter of the triangle. It lies inside for an acute and outside for an obtuse triangle. Altitudes are nothing but the perpendicular line ( AD, BE and CF ) from one side of the triangle ( either AB or BC or CA ) to the opposite vertex.
Why scissor is Hinge Theorem?
This theorem is called the “Hinge Theorem” because it acts on the principle of the two sides described in the triangle as being “hinged” at their common vertex.