Geometry: Construction-Triangle whose base, vertical angle and altitude are given

Geometric Construction: Triangle whose base, vertical angle and altitude are given
Steps:-
 Step I: Draw a line segment equal to the base BC (say). Step II: Below BC, make an CBP at B equal to the vertical angle of the triangle. Step III: Draw a line BE BP at the point B. Step IV: Draw the right bisector QR of BC meeting line BE at O and BC at M. Step V: With 0 as centre and OB as radius draw a circle. Step VI: Take a point N on QR such that MN is equal to the altitude of the triangle. Step VII: Draw a line parallel to BC through point N, intersecting circle drawn in step V at A and A'. Step VIII: Join AB, AC and A'B, A'C to obtain triangles ABC and A'BC as the required triangles.
 People who saw this lesson also found the following lessons useful: Construction: Triangle with base, vertical angle given Slope Equation Circumcircles Complementary Angles Problems on Age
Example: Construct ABC in which BC = 6 cm, A = 60 and the altitude through A is 4.5 cm. Measure the length of the median through A. Write the steps of construction.
 Solution: Steps of Construction Step I: Draw a line segment BC = 6 cm. Step II: Below BC, make CBP = BAC = 60 Step III: Draw a line BE X BP at point B. Step IV: Draw perpendicular bisector QR of BC. Suppose it meets BE at O and at BC at M. Step V: With O as centre and OB as radius draw a circle. Step VI: Take a point N on QR such that MN = 4.5 cm(altitude through A). Step VII: Draw a line through N parallel to BC,intersecting the circle at A and A'. Step VIII: Join AB, AC and A' B, A'C. Either of the triangles ABC, A'BC is the required triangle. To find Median through A, join A to the mid-point M of BC. By measuring AM, it comes AM = 5 cm.

 As many of you know, Winpossible's online courses use a unique teaching method where an instructor explains the concepts in any given area to you in his/her own voice and handwriting, just like you see your teacher explain things to you on a blackboard in your classroom. All our courses include teacher's instruction, practice questions as well as end-of-lesson quizzes for practice. You can enroll in any of our online courses by clicking here. The format of Winpossible's online courses is also very suitable for teachers who are using an interactive whiteboard such as Smartboard on Promethean in their classrooms, because the course lessons can be easily displayed on such interactive whiteboards. Volume pricing is available for schools interested in our online courses. For more information, please contact us at educators@winpossible.com.

 Copyright © Winpossible, 2010 - 2011 Best viewed in 1024x768 & IE 5.0 or later version