Construct a rhombus ABCD in which AB= 6 cm and angle ABC= 60degree. Divide it into two triangle ABC and ADC. Construct a triangle AB 'C ' similar to triangle ABC with scale factor 2/3. Draw a line segment C 'D ' parallel to CD, where D ' lies on AD. Is AB 'C 'D ' a rhombus
Construct a triangle ABC having line AB=70mm and angle AB=75 andCAB=60 respectively and inscribe the triangle
To construct the rhombus ABCD and the subsequent steps, follow these instructions:
Step 1: Draw a line segment AB of length 6 cm.
Step 2: From point A, draw a ray AX making a 60-degree angle with AB.
Step 3: With point B as the center, draw an arc intersecting the ray AX at point C.
Step 4: Draw a line segment BC connecting points B and C.
Step 5: Extend line segment BC to point D, where AD is parallel to BC.
You have now constructed rhombus ABCD with the given specifications.
Step 6: To divide rhombus ABCD into triangles ABC and ADC:
- Draw a line segment AC connecting points A and C, dividing the rhombus into two triangles.
Step 7: To construct triangle AB'C' similar to triangle ABC with a scale factor of 2/3:
- From point A, measure a length of (2/3) times AB, which is 2/3 * 6 = 4 cm.
- From point B, draw a ray BY making a 60-degree angle with AB.
- With point B as the center, draw an arc intersecting the ray BY at point C'.
- Draw a line segment B'C' connecting points B and C'.
Step 8: To draw a line segment C'D' parallel to CD, where D' lies on AD:
- From point C', draw a line parallel to CD (this can be achieved using a ruler and a compass to ensure parallelism).
- Extend this line to intersect line AD at point D'.
Step 9: Finally, determine if AB'C'D' is a rhombus:
- A rhombus has the following properties: All sides are equal in length, and opposite angles are equal.
- Measure the length of each side of AB'C'D' to check if they are all equal.
- Measure the angles at B' and C' to verify if they are equal.
- If all sides are equal in length and the opposite angles are equal, then AB'C'D' is a rhombus.