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1. Carefully prove the theorem: The sum of the distances from any interior point P to the sides of an equilateral triangle is equal to the length of the triangle's altitude. Hint: Begin by partitioning AABC into three triangles based on the interior point P. Then express the area of AABC as the sum of the areas of these three internal ones. Conclude that the height of AABC is 1+m+n. n m

1. Carefully prove the theorem: The sum of the distances from any interior point P to the sides of an equilateral triangle is equal to the length of the triangle's altitude. Hint: Begin by partitioning AABC into three triangles based on the interior point P. Then express the area of AABC as the sum of the areas of these three internal ones. Conclude that the height of AABC is 1+m+n. n m

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5:51 PM Mon Sep 5 X WS2 F2022.pdf MATH 119 WORKSHEET 2 1. Carefully prove the theorem: The sum of the distances from any interior point P to the sides of an equilateral triangle is equal to the length of the triangle's altitude. ●●● Solve the following problems on a separate page. Justify your answers to earn full credit. Hint: Begin by partitioning AABC into three triangles based on the interior point P. Then express the area of AABC as the sum of the areas of these three internal ones. Conclude that the height of AABC is 1+m+n. (I.e., show that in the figure.) 2. Let D be that point on side BC of AABC such that AD is the bisector of ZBAC. Prove that ZADC is half the sum of the interior angle at B and the exterior angle at C. ZADC = B + ε 2 3. Given that LN 1 PR and that O is the center of the circle PLR, then use a theorem previously discussed in class to prove that LM = NM. Justify each step in your solution. P B B September 2, 2022 a D M N E C R B 95%
Transcribed Image Text:5:51 PM Mon Sep 5 X WS2 F2022.pdf MATH 119 WORKSHEET 2 1. Carefully prove the theorem: The sum of the distances from any interior point P to the sides of an equilateral triangle is equal to the length of the triangle's altitude. ●●● Solve the following problems on a separate page. Justify your answers to earn full credit. Hint: Begin by partitioning AABC into three triangles based on the interior point P. Then express the area of AABC as the sum of the areas of these three internal ones. Conclude that the height of AABC is 1+m+n. (I.e., show that in the figure.) 2. Let D be that point on side BC of AABC such that AD is the bisector of ZBAC. Prove that ZADC is half the sum of the interior angle at B and the exterior angle at C. ZADC = B + ε 2 3. Given that LN 1 PR and that O is the center of the circle PLR, then use a theorem previously discussed in class to prove that LM = NM. Justify each step in your solution. P B B September 2, 2022 a D M N E C R B 95%
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