1. **Problem:** Draw a line AB 60 mm long and bisect it. **Step 1:** Draw a straight line segment AB of length 60 mm. **Step 2:** To bisect AB, find the midpoint M such that AM = MB = 30 mm. **Step 3:** Use a compass to draw arcs from points A and B with radius greater than half of AB, intersecting above and below the line. **Step 4:** Draw a line through the intersection points of the arcs; this line bisects AB at M. 2. **Problem:** Draw a line AB 165 mm long and divide it in the proportion 3:4:2. **Step 1:** Draw line AB of length 165 mm. **Step 2:** The total parts are 3 + 4 + 2 = 9 parts. **Step 3:** Each part length = $\frac{165}{9} = 18.33$ mm. **Step 4:** Mark points dividing AB at distances 3 parts (55 mm) and 7 parts (128.33 mm) from A. 3. **Problem:** Construct angles by bisection using 45° and 60° set squares. **Step 1:** Use 45° and 60° angles as starting points. **Step 2:** Bisect angles repeatedly to get half angles like 22.5°, 30°, 15°, etc. **Step 3:** Combine angles to form required angles: - (a) 22.5° is half of 45°. - (b) 150.5° = 180° - 29.5° (construct 30° and bisect slightly). - (c) 52.5° = 45° + 7.5° (bisect 15°). - (d) 112.5° = 90° + 22.5°. - (e) 37.5° = 45° - 7.5°. - (f) 146.5° = 135° + 11.5° (bisect 23°). 4. **Problem:** Construct triangle ABCD with AB=89 mm, AC=76 mm, angle CAB=67.5°, and draw inscribed circle. **Step 1:** Draw base AB = 89 mm. **Step 2:** At A, construct angle CAB = 67.5° using bisection. **Step 3:** From A along angle, mark point C at 76 mm. **Step 4:** Connect B to C to complete triangle ABC. **Step 5:** Draw angle bisectors of triangle ABC; their intersection is the incenter. **Step 6:** Draw inscribed circle centered at incenter tangent to all sides. 5. **Problem:** Construct triangle ABC with AB=70 mm, AC=57 mm, BC=76 mm and draw circumscribing circle. **Step 1:** Draw base AB = 70 mm. **Step 2:** Using compass, draw arcs from A with radius 57 mm and from B with radius 76 mm; their intersection is point C. **Step 3:** Connect A to C and B to C. **Step 4:** Draw perpendicular bisectors of sides; their intersection is circumcenter. **Step 5:** Draw circumscribing circle centered at circumcenter passing through A, B, and C. Final note: These are classical geometric constructions using compass and straightedge principles.