Question

Every building you spend time in––schools, libraries, houses, apartment complexes, movie theaters, and even your favorite ice cream shop––is the product of mathematical principles applied to design and construction. Have you ever wondered how building professionals incorporate math to create the common structures you walk in and out of every day? Whenever an architect has to draw a plan for a multistoried building, they have to draw intersecting lines and parallel lines at different angles. Without the knowledge of the properties of these lines and angles, do you think they can draw the layout of the building? Before construction workers can build a habitable structure, an architect has to design it. Geometry, algebra, and trigonometry all play a crucial role in architectural design. Architects apply these math forms to plan their blueprints or initial sketch designs. Taj Mahal is one of the most beautiful architectural heritage and is so mathematically accurate and symmetrical. It highlights the use of mathematics in ancient architecture. Look at the above figure and answer the following questions: Q.1) In figure, if AB and CD are parallel lines cut by transversal PQ, name the pair of : (1X 5 = 5 marks) Vertically opposite angles Alternate interior angles Alternate exterior angles Corresponding angles Co interior angles Q.2) In figure , LM || ST and LMQ=85⁰, find STQ. (2 marks) Q.3) Give at least three mathematical concepts used in construction of Taj Mahal, relating it to topic lines and angles. (3 marks) Q.4) What is an adjacent angle? Give two examples from figure. (3 marks) Q.5) Prove that sum of angles of ∆ PCD (in fig.) is 180⁰. (3 marks) Q.6) In figure, if AB || CD cut by transversal PQ show that bisectors of two pairs of interior angles encloses a rectangle. (4 marks)

Answer 1

Answer:

Taj Mahal ................................