how to construct a quadrilateral MATH where MT bisects M. AH is perpendicular bisector of MT. M is 60 degrees. A is 120 degrees. MH is 8cm
Make a sketch of your finished quad and enter all the information.
Notice that adjacent angles add up to 180°, so AT || MH, and it is easy to see that MAH must be an equilateral triangle.
You should see that MATH must be a rhombus, with all sides equal to 8 cm
I assume you know how to construct a 60° angle with compass and straightedge.
The rest is easy.
To construct a quadrilateral MATH where MT bisects M and AH is the perpendicular bisector of MT, we can follow these steps:
Step 1: Draw a line segment MH of length 8 cm.
Step 2: At the point H, draw a perpendicular line AH. Make sure AH is of sufficient length to construct the quadrilateral.
Step 3: Using a protractor, measure an angle of 60 degrees at the point M. Draw a line segment from M that makes this angle.
Step 4: Bisect the angle M using a compass. Place the compass point on M and draw an arc that intersects the line on both sides of the angle. Label the points of intersection as X and Y.
Step 5: Without changing the compass width, place the compass point on X and draw an arc that intersects the line. Label this point of intersection as T.
Step 6: Draw a line segment from T to H. This line segment will bisect the angle M and also pass through the point H.
Step 7: Now, draw a line segment from A to T. This line segment represents the side of the quadrilateral.
Step 8: Finally, complete the quadrilateral by drawing a line segment from H to A.
Now you have constructed the quadrilateral MATH, where MT bisects M and AH is the perpendicular bisector of MT. The angles at M and A are 60 degrees and 120 degrees respectively, and the side MH is 8 cm.