Answer:
Explanation:
To find the measures of SH and TH, we can use the information given in the problem.
We are told that H is the centroid of the triangle ASTR. This means that the centroid is the point of concurrency of the medians of the triangle. In this case, EH, DH, and SM are the medians.
We are also given the lengths of EH, DH, and SM. EH is 6 units, DH is 4 units, and SM is 24 units.
To find the measure of SH, we need to find the length of the segment SH. Since H is the centroid, we know that the length of the median EH is twice the length of the segment SH. Therefore, SH is half the length of EH, which is 6/2 = 3 units.
To find the measure of TH, we need to find the length of the segment TH. Since H is the centroid, we know that the length of the median DH is twice the length of the segment TH. Therefore, TH is half the length of DH, which is 4/2 = 2 units.
So, the measures are:
A. SH = 3 units
B. TH = 2 units
Now, let's consider the Exterior Angle Inequality Theorem. This theorem states that the measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.
In this problem, we need to determine which angles satisfy the given conditions.
A. To find angles that measure less than angle 21, we need to find the remote interior angles of angle 21. Since angle 21 is an interior angle of triangle ASTR, its remote interior angles are angles 7 and 14. Therefore, any exterior angle that is less than angle 7 or angle 14 will satisfy this condition.
B. To find angles that measure less than angle 29, we need to find the remote interior angles of angle 29. Since angle 29 is an interior angle of triangle ASTR, its remote interior angles are angles 12 and angle 17. Therefore, any exterior angle that is less than angle 12 or angle 17 will satisfy this condition.
C. To find angles that measure greater than angle 25, we need to find the remote interior angles of angle 25. Since angle 25 is an interior angle of triangle ASTR, its remote interior angles are angles 1 and angle 6. Therefore, any exterior angle that is greater than angle 1 or angle 6 will satisfy this condition.
D. To find angles that measure greater than angle 28, we need to find the remote interior angles of angle 28. Since angle 28 is an interior angle of triangle ASTR, its remote interior angles are angles 6 and angle 12. Therefore, any exterior angle that is greater than angle 6 or angle 12 will satisfy this condition.
I hope this helps! Let me know if you have any other questions.