The relationship between the diagonals of a parallelogram—representing the sum and difference of its spanning sides—reveals that they are orthogonal only when the sides have equal magnitudes. The sources explain that the algebraic identity governing these diagonals ensures their dot product reaches zero only when the side lengths are identical, a condition that transforms a general parallelogram into a rhombus. While unequal sides result in oblique intersections, matching side lengths force a perpendicular crossing, which can be visually demonstrated as the intersection angle hits exactly ninety degrees. This geometric principle serves as a practical magnitude check, as it confirms that the only way for these internal lines to be perpendicular is for the outer sides to be of equal length.
block-beta
columns 5
CC["Criss-Cross"]:5
%% Condensed Notes
CN["Condensed Notes"]:5
RF["Relevant File"]:5
NV["Narrated Video"]:4 VO["Voice-over"]
PA("Plotting & Analysis")AA("Animation & Analysis")KT("Summary & Interpretation") ID("Illustration & Demo") PO("Polyptych")
%% Proof and Derivation
PD["Proof and Derivation"]:5
AF("Derivation Sheet"):5
NV2["Narrated Video"]:4 VO2["Voice-over"]
PA2("Plotting & Analysis")AA2("Animation & Analysis")KT2("Summary & Interpretation") ID2("Illustration & Demo") PO2("Polyptych")
classDef color_1 fill:#8e562f,stroke:#8e562f,color:#fff
class CC color_1
%% %% Condensed Notes
classDef color_2 fill:#14626e,stroke:#14626e,color:#14626e
class CN color_2
class RF color_2
classDef color_3 fill:#1e81b0,stroke:#1e81b0,color:#1e81b0
class NV color_3
class PA color_3
class AA color_3
class KT color_3
class ID color_3
classDef color_4 fill:#47a291,stroke:#47a291,color:#47a291
class VO color_4
class PO color_4
%% Proof and Derivation
classDef color_5 fill:#307834,stroke:#307834,color:#fff
class PD color_5
class AF color_5
classDef color_6 fill:#38b01e,stroke:#38b01e,color:#fff
class NV2 color_6
class PA2 color_6
class AA2 color_6
class KT2 color_6
class ID2 color_6
classDef color_7 fill:#47a291,stroke:#47a291,color:#fff
class VO2 color_7
class PO2 color_7
‣