Figure 121 : Heights of triangle
Q01. Diagram
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Coordinate geometry 
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Q02. Heights of triangle of triangle are concurrent
Construction
- Draw triangle ABC
- Draw height AP perpendicular to BC
- Draw height BQ perpendicular to CA
- Draw height CR perpendicular to AB
- Heights are concurrent at O which is called ortho-center
- For proof
- Draw DF parallel to BC and passing A
- Draw FE parallel to CA and passing B
- Draw DE parallel to AB and passing C
- AC parallel to BE and CE parallel to AB
- Hence ABEC is a parallelogram
- Hence BE = AC
- Similarly, ACBF is a parallelogram
- Hence BF = AC
- Hence B is midpoint of EF
- Similarly, C is midpoint of DE and A is midpoint of DF
- Hence O is the circum center of triangle DEF
- Hence O is the ortho-center of triangle ABC
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Q03. Pedal triangle
- Let P,Q,R make a triangle
- Triangle PQR is the pedal triangle of triangle ABC
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Q04. Reference
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Q05 Questions
- 1. What is the height of a triangle ?
- 2. What is a pedal triangle of a triangle ?
- 3. Construct the triangle if 3 heights are given
- 4. What is the meaning fo the triangle heights are concurrent ?
- 5. What is the ortho-center of a triangle ?
- 6. What is the meaning of colinear ?
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