Discovering and Proving Polygon Properties
... Students explore two kinds of parallelograms, rhombuses and rectangles, as well as squares, which are both rhombuses and rectangles. Students discover properties of all types of quadrilaterals, including how their diagonals are related. In the case of trapezoids, students investigate midsegments, wh ...
... Students explore two kinds of parallelograms, rhombuses and rectangles, as well as squares, which are both rhombuses and rectangles. Students discover properties of all types of quadrilaterals, including how their diagonals are related. In the case of trapezoids, students investigate midsegments, wh ...
Warm-Up Determine the triangle relationship.
... • If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the two triangles are congruent. ...
... • If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the two triangles are congruent. ...
topic 2-3: identifying similar triangles
... When polygons are similar, two criteria must be met: 1) Corresponding angles are ____________________. 2) Corresponding sides are ___________________________. However…if you don’t know the measures of all sides and angles, is there another way to tell? There are several theorems that allow us to sho ...
... When polygons are similar, two criteria must be met: 1) Corresponding angles are ____________________. 2) Corresponding sides are ___________________________. However…if you don’t know the measures of all sides and angles, is there another way to tell? There are several theorems that allow us to sho ...
Lesson 2 Reteach Triangles
... Every triangle has at least two acute angles. One way you can classify a triangle is by using the third angle. Another way to classify triangles is by their sides. Classify Triangles Using Angles ...
... Every triangle has at least two acute angles. One way you can classify a triangle is by using the third angle. Another way to classify triangles is by their sides. Classify Triangles Using Angles ...
File
... Learner Objective: Students will solve proofs and problems using the HL Postulate of triangle congruence. ...
... Learner Objective: Students will solve proofs and problems using the HL Postulate of triangle congruence. ...
9-Similarity File
... Determine if the triangles are similar. If so, write the similarity statement and the similarity ratio. ...
... Determine if the triangles are similar. If so, write the similarity statement and the similarity ratio. ...
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.