Question
construct a quadrilateral EFGHin which EFis equal to 4.5 CM and FG is equal to 4.5 CM and GH is equal to 5.2 CM and HE
is equal to 4.9 cm and angle F G H is equal to 105 degree
is equal to 4.9 cm and angle F G H is equal to 105 degree
Answers
Answered by
GPT-4o mini
To construct a quadrilateral EFGH with the given dimensions and angle, follow these steps:
1. **Draw Line Segment EF:**
- Start by drawing a line segment EF that measures 4.5 cm.
2. **Draw Line Segment FG:**
- From point F, measure a distance of 4.5 cm and draw an arc. This will help in creating point G.
- The angle ∠FGH will be constructed starting from point F.
3. **Construct Angle FGH:**
- With a protractor, measure and mark an angle of 105 degrees at point F (where the line FG will extend).
- Draw a ray from F at this angle (105 degrees from the line EF). We will mark the line FG as it extends from F.
4. **Determine Point G:**
- From F, mark point G at 4.5 cm along the ray.
5. **Draw Line Segment GH:**
- Now, from point G, measure 5.2 cm. Mark a point along this segment, and draw an arc at this distance.
6. **Draw Line Segment HE:**
- Now we need to find point H such that HE = 4.9 cm.
- From point E, draw an arc with a radius of 4.9 cm to locate point H.
7. **Complete the Quadrilateral:**
- Now, connect points H and G to complete the quadrilateral. Ensure that both segments HE and GH are drawn to their respective lengths.
After following these steps, you will have successfully constructed the desired quadrilateral EFGH with the specified dimensions and angle. Adjust your drawing carefully to ensure accuracy in the measurements and angles.
1. **Draw Line Segment EF:**
- Start by drawing a line segment EF that measures 4.5 cm.
2. **Draw Line Segment FG:**
- From point F, measure a distance of 4.5 cm and draw an arc. This will help in creating point G.
- The angle ∠FGH will be constructed starting from point F.
3. **Construct Angle FGH:**
- With a protractor, measure and mark an angle of 105 degrees at point F (where the line FG will extend).
- Draw a ray from F at this angle (105 degrees from the line EF). We will mark the line FG as it extends from F.
4. **Determine Point G:**
- From F, mark point G at 4.5 cm along the ray.
5. **Draw Line Segment GH:**
- Now, from point G, measure 5.2 cm. Mark a point along this segment, and draw an arc at this distance.
6. **Draw Line Segment HE:**
- Now we need to find point H such that HE = 4.9 cm.
- From point E, draw an arc with a radius of 4.9 cm to locate point H.
7. **Complete the Quadrilateral:**
- Now, connect points H and G to complete the quadrilateral. Ensure that both segments HE and GH are drawn to their respective lengths.
After following these steps, you will have successfully constructed the desired quadrilateral EFGH with the specified dimensions and angle. Adjust your drawing carefully to ensure accuracy in the measurements and angles.