Question

for exercises 9 - 15, tell whether the statement is true or false. for each false statement, sketch a count explain why the statement is false. 11. an acute angle is an angle whose measure is less than 90°. true or false 12. if two lines intersect to form a right angle, then the lines are perpendicular. true or false 13. a diagonal is a line segment that connects any two vertices of a polygon. true or false 14. a ray that divides the angle into two angles is the angle bisector. true or false 15. an obtuse triangle has exactly one angle whose measure is greater than 90°. true or fa

Explanation:

1. By definition, an acute angle has a measure less than 90°, so it's true.
2. Perpendicular lines are defined as lines that intersect to form a right - angle, so it's true.
3. A diagonal connects non - adjacent vertices of a polygon. Connecting any two vertices includes the sides of the polygon, so this is false.
4. An angle bisector is a ray that divides an angle into two congruent angles. Just dividing into two angles is not enough, so this is false.
5. By the definition of an obtuse triangle, it has exactly one angle with a measure greater than 90°, so it's true.

Answer:

1. TRUE
2. TRUE
3. FALSE
4. FALSE
5. TRUE