Grade 6 Geometrical Constructions

Step 1: Draw a straight line:

Using a ruler, draw a straight line on your paper.

Step 2: Mark the starting point:

Mark a point A on the line as the starting point.

Step 3: Measure 5 cm:

Using the ruler, measure 5 cm from point A and mark point B.

Step 4: Draw the line segment:

Connect points A and B with a straight line. Label it as line segment AB.

Step 5: Verify:

Measure AB with the ruler to ensure it is exactly 5 cm.

Step 1: Draw the line segment:

Draw a line segment AB of length 6 cm using a ruler.

Step 2: Set the compass:

Set the compass to a width greater than half of AB (e.g., 4 cm).

Step 3: Draw arcs from point A:

With the compass point at A, draw two arcs above and below the line segment.

Step 4: Draw arcs from point B:

Without changing the compass width, place the compass point at B and draw two arcs intersecting the previous arcs above and below the line.

Step 5: Draw the bisector:

Connect the intersection points of the arcs with a straight line. This line is the perpendicular bisector of AB, intersecting AB at its midpoint.

Step 1: Draw a base line:

Draw a straight line and mark a point O on it as the vertex.

Step 2: Draw an arc:

With the compass point at O, draw an arc intersecting the line at point P.

Step 3: Draw a second arc:

Without changing the compass width, place the compass point at P and draw another arc above the line, intersecting the first arc at point Q.

Step 4: Draw the angle:

Draw a straight line from O to Q. The angle \( \angle POQ = 60^\circ \).

Step 5: Verify:

Use a protractor to confirm that \( \angle POQ \) is 60°.

Step 1: Draw the angle:

Draw a 70° angle \( \angle AOB \) using a protractor, with O as the vertex.

Step 2: Draw an arc:

With the compass point at O, draw an arc intersecting OA at P and OB at Q.

Step 3: Draw arcs inside the angle:

Place the compass point at P and draw an arc inside the angle. Then, with the same compass width, place the compass point at Q and draw another arc intersecting the previous arc at point R.

Step 4: Draw the bisector:

Draw a straight line from O to R. The line OR bisects \( \angle AOB \), so \( \angle AOR = \angle ROB = 35^\circ \).

Step 5: Verify:

Use a protractor to confirm that \( \angle AOR \) and \( \angle ROB \) are each 35°.

Step 1: Check triangle inequality:

4 + 5 > 6 (9 > 6), 4 + 6 > 5 (10 > 5), 5 + 6 > 4 (11 > 4). All conditions are satisfied.

Step 2: Draw the base:

Draw a line segment AB of 6 cm (the longest side).

Step 3: Draw an arc for the second side:

With the compass set to 5 cm, place the point at A and draw an arc above AB.

Step 4: Draw an arc for the third side:

With the compass set to 4 cm, place the point at B and draw an arc intersecting the previous arc at point C.

Step 5: Complete the triangle:

Draw lines from A to C and B to C to form triangle ABC.