Constructions — Karnataka (SSLC) Class 9 Mathematics Solutions (Free)

Step 1: Draw line segment AB = 7 cm using straightedge and compass. Step 2: Set compass to more than half the length of AB (e.g., 4 cm). Step 3: From point A, draw an arc above and below the line AB. Step 4: From point B with the same compass radius, draw arcs above and below the line AB, intersecting the first two arcs at points P and Q. Step 5: Join P and Q using straightedge. Line PQ is the perpendicular bisector of AB. Verification: Any point on PQ is equidistant from A and B. The perpendicu…

Step 1: Draw an angle of 60° with vertex at O. (Use compass: draw arc of any radius from O intersecting both rays at A and B. From A and B with same radius, draw intersecting arc at C. Angle AOC = 60°.) Step 2: From vertex O, set compass to any convenient radius and draw an arc intersecting both rays of the angle at points P and Q. Step 3: From point P, set compass to more than half of PQ and draw an arc inside the angle. Step 4: From point Q with the same compass radius, draw an arc inside the …

Step 1: Draw base BC = 6 cm using straightedge and compass. Step 2: From B, set compass to 5 cm radius and draw an arc above BC. Step 3: From C, set compass to 5 cm radius and draw an arc above BC intersecting the first arc at point A. Step 4: Join AB and AC. Triangle ABC is isosceles with AB = AC = 5 cm and BC = 6 cm. Step 5: To construct altitude from A (vertex angle) to BC: the altitude is perpendicular from A to line BC. Step 6: From A, set compass to more than the perpendicular distance to …

Step 1: Draw line segment PQ = 9 cm using straightedge and compass. Step 2: Draw a ray at acute angle from P, different from PQ. Call it PR. Step 3: Using compass with any radius, mark 3 equal divisions (since ratio is 2:1, total parts = 3) on ray PR from P. Mark points P₁, P₂, P₃ where PP₁ = P₁P₂ = P₂P₃. Step 4: Join P₃Q using straightedge. Step 5: From P₂, construct a line parallel to P₃Q using compass and straightedge. Step 6: This parallel line intersects PQ at point M. Point M divides PQ in…

Step 1: Draw base BC = 7 cm using straightedge and compass. Step 2: At point B, construct a 45° angle. (Use compass: first construct 90° by perpendicular bisector method at B. Then bisect the 90° angle using angle bisector to get 45°.) Step 3: On the 45° ray from B, measure 6 cm using compass and mark point A. Step 4: Join A and C using straightedge to complete triangle ABC. Verification: AB = 6 cm, BC = 7 cm, angle ABC = 45°. Final Answer: Triangle ABC with sides AB = 6 cm, BC = 7 cm and includ…