Answer:
True: 1, 3, 5
Step-by-step explanation:
The diagram shows the rhombus with the side length of 4 inches.
Properties:
- opposite angles of the rhombus are congruent;
- diagonals of the rhombus bisect each other;
- diagonals of the rhombus bisect rhombus angles;
- diagonals are perpendicular;
- diagonals divide the rhombus into four congruent right triangles with legs that are halves of diagonals.
Consider right triangle (bottom left right triangle) with the hypotenuse of 4 in and acute angle 30°. In this triangle, leg opposite to the 30° angle is half of hypotenuse and is 2 in. By the Pythagorean theorem,
So, option 2 is false.
The second acute angle of this triangle has the measure
So, option 1 is true.
The perimeter of the rhombus is the sum of all sides, so
Option 3 is true.
The measures of the rhombuses angles are
Thus, option 4 is false.
The length of the longer diagonal is
Option 5 is true.