Aquilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonals is equal to the side length of the rhombus.
which measures are true for the quilt piece? check all that apply.
1.a = 60°
2.x = 3 in.
3.the perimeter of the rhombus is 16 inches.
4.the measure of the greater interior angle of the rhombus is 90°.
5.the length of the longer diagonal is approximately 7 inches.

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.

Options 1, 3 and 5 are correct.

Step-by-step explanation:

Option 1.

In the triangle ABO,

30° + 90° + ∠ABO = 180° [ Since diagonals of rhombus intersect at 90°]

∠ABO = 180 - 120 = 60°

Therefore, m∠a = 60° [Since opposite angles of rhombus are always equal]

Option 1 is correct.

Option 2.

Since AO = OC = x [Diagonals of trapezoid bisect each other]

In the triangle AOB,

x² + 2² = 4² [By Pythagoras theorem]

[By the property of trapezoid diagonal intersect each other at 90°]

x² = 16 - 4

x = √12

x = 2√3

Therefore, option 2 is incorrect.

3. Perimeter of the rhombus = 4 + 4 + 4 + 4 = 12

Option 3 is correct.

4. Measure of greater interior angle is = 2 × 60° = 120°

Therefore, option 4 is incorrect.

5.  Longer diagonal of the rhombus = 2

= 2 × (2√3)

= 4√3

= 6.92

≈ 7 inches

Therefore, option 5 is correct .                                                        

A’b’c’ are the coordinates to the new location of the transformed triangle abc. find the distance between the coordinates points to use for your calculations.

Sin(a)+cos(a)+cot(a)-1=2(csc(x)+1)