5 blog notes for congruent triangle proofs
... same SHAPE (similar), but does NOT work to also show they are the same size, thus congruent! Consider the example at the right. ...
... same SHAPE (similar), but does NOT work to also show they are the same size, thus congruent! Consider the example at the right. ...
Discovering Properties of Kites
... of Kites A kite is a quadrilateral having two pairs of distinct congruent sides, as illustrated in the figure at the right. It’s a square with one vertex moved away from its opposite vertex. The longest diagonal of the kite is the major diagonal and the other diagonal is the minor diagonal. The angl ...
... of Kites A kite is a quadrilateral having two pairs of distinct congruent sides, as illustrated in the figure at the right. It’s a square with one vertex moved away from its opposite vertex. The longest diagonal of the kite is the major diagonal and the other diagonal is the minor diagonal. The angl ...
Exploring Congruent Triangles
... Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent ...
... Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent ...
Triangles
... three of its sides are equal. 6. A triangle that has no equal sides is a ______________ triangle. ...
... three of its sides are equal. 6. A triangle that has no equal sides is a ______________ triangle. ...
then the 2 triangles are CONGRUENT! - Home
... SWBAT justify that two triangles are congruent using the congruence postulate theorems. ...
... SWBAT justify that two triangles are congruent using the congruence postulate theorems. ...
G eome try - Net Texts
... Leg-Leg (LL) Theorem: If the legs of two right triangles are congruent, then the triangles are congruent. Angle-Leg (AL) Theorem: If an angle and a leg of a right triangle are congruent to those of another right triangle, then the two triangles are congruent. Hypotenuse-Angle (HA) Theorem: If an ang ...
... Leg-Leg (LL) Theorem: If the legs of two right triangles are congruent, then the triangles are congruent. Angle-Leg (AL) Theorem: If an angle and a leg of a right triangle are congruent to those of another right triangle, then the two triangles are congruent. Hypotenuse-Angle (HA) Theorem: If an ang ...
Penrose tiling
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right. A Penrose tiling has many remarkable properties, most notably:It is non-periodic, which means that it lacks any translational symmetry. It is self-similar, so the same patterns occur at larger and larger scales. Thus, the tiling can be obtained through ""inflation"" (or ""deflation"") and any finite patch from the tiling occurs infinitely many times.It is a quasicrystal: implemented as a physical structure a Penrose tiling will produce Bragg diffraction and its diffractogram reveals both the fivefold symmetry and the underlying long range order.Various methods to construct Penrose tilings have been discovered, including matching rules, substitutions or subdivision rules, cut and project schemes and coverings.