Question 4 - Constructing Triangle - Given sum of 3 sides and 2 base angles - Constructions

Transcript

Question 4 Construct a triangle ∆XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm. Given ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm. Let’s construct Δ XYZ Steps of Construction : Draw a line segment AB equal to XY + YZ + ZX = 11 cm. Make angle equal to ∠ Y = 30° from point A Let the angle be ∠ LAB. Make angle equal to ∠Z = 90° from point B Let the angle be ∠ MBA 4. Bisect ∠ LAB and ∠ MBA. Let these bisectors intersect at a point X . 5. Make perpendicular bisector of XA Let it intersect AB at point Y 6. Make perpendicular bisector of XB Let it intersect AB at point Z 7. Join XY & XZ ∴ Δ XYZ is the required triangle