1 / 7

Identifying and Using Theorems for Parallelograms in Architecture

Learn how to identify and use theorems to determine if a quadrilateral is a parallelogram in architectural structures, with examples and guided practice.

josedaniel
Download Presentation

Identifying and Using Theorems for Parallelograms in Architecture

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ARCHITECTURE In the photograph, ST UVand ST UV. By Theorem 8.9, quadrilateral STUVis a parallelogram. EXAMPLE 2 Identify a parallelogram The doorway shown is part of a building in England. Over time, the building has leaned sideways. Explain how you know that SV =TU. SOLUTION By Theorem 8.3, you know that opposite sides of a parallelogram are congruent. So, SV = TU.

  2. For what value of xis quadrilateral CDEFa parallelogram? ALGEBRA By Theorem 8.10, if the diagonals of CDEFbisect each other, then it is a parallelogram. You are given that CNEN. Find xso that FN DN. EXAMPLE 3 Use algebra with parallelograms SOLUTION

  3. ANSWER Quadrilateral CDEF is a parallelogram when x = 4. EXAMPLE 3 Use algebra with parallelograms DN FN = Set the segment lengths equal. 3x 5x – 8 = Substitute 5x –8 for FN and 3xfor DN. 0 2x – 8 = Subtract 3xfrom each side. 8 2x = Add 8 to each side. 4 x = Divide each side by 2. FN = 5(4) –8 = 12 andDN = 3(4) = 12. Whenx = 4,

  4. 2. ANSWER Theorem 8.9 for Examples 2 and 3 GUIDED PRACTICE What theorem can you use to show that the quadrilateral is a parallelogram?

  5. 3. ANSWER Theorem 8.7 for Examples 2 and 3 GUIDED PRACTICE What theorem can you use to show that the quadrilateral is a parallelogram?

  6. What theorem can you use to show that the quadrilateral is a parallelogram? 4. ANSWER Theorem 8.8 for Examples 2 and 3 GUIDED PRACTICE

  7. 5. For what value of xis quadrilateral MNPQa parallelogram? Explain your reasoning. 2; The diagonals of a parallelogram bisect each other so solve 2x = 10 – 3x forx. ANSWER for Examples 2 and 3 GUIDED PRACTICE

More Related