High School

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### Part A: Answer the following statements with "Always True," "Sometimes True," or "Never True."

1. A square is a rectangle. ______________
2. A rhombus is a square. ______________
3. A parallelogram is a square. ______________
4. A rectangle is a rhombus. ______________
5. A parallelogram is a square. ______________
6. A parallelogram is a rectangle. ______________
7. A quadrilateral is a parallelogram. ______________
8. A square is a rectangle and a rhombus. ______________
9. An equilateral quadrilateral is a rhombus. ______________
10. An equiangular quadrilateral is a rectangle. ______________

### Part B: Find the missing measure. Use the space below for your solution. Given that ABCD is a parallelogram, AC and BD are diagonals.

1. If \(a = 80^\circ\) and \(b = 11x + 10\), then \(m_d =\) ________ and \(m_c =\) _________
2. If \(d = 9x + 15\) and \(a = 6x + 15\), then \(m_b =\) ______ and \(m_c =\) _______
3. If \(b = 35^\circ\) and \(c = 14x + 5\), then \(m_d =\) ________ and \(m_a =\) ________
4. If \(AB = 2x + 15\) and \(DC = x + 25\), then \(AB =\) _________ and \(DC =\) ________
5. If \(AE = 3x + 3\) and \(EC = 4x + 4\), then \(AE =\) ________, \(AC =\) _________
6. If \(JG = 4x + 4\) and \(FH = 2x + 10\), find \(x =\) _______, \(JG =\) __________, \(FH =\) __________
7. If \(AD = 3x + 7\) and \(BC = 2x + 5\), find \(x =\) _______, \(AD =\) __________, \(BC =\) __________
8. If \(a = 80^\circ\), then \(b =\) ______ and \(c =\) ____________
9. If \(AB = 8 \text{ cm}\), then \(DC =\) _______________
10. If \(DE = 5 \text{ cm}\), then \(EB =\) __________ and \(DB =\) _____________
11. If \(AC = 30 \text{ inches}\), then \(AE =\) ______ and \(EC =\) __________
12. If \(AE = 3x + 2\) and \(EC = x + 10\), find \(x =\) _______, \(AE =\) _______, \(EC =\) _______, \(AC =\) _______

### Part C: Choose the correct answer.

1. a. \(95^\circ\) b. \(85^\circ\) c. \(75^\circ\) d. \(70^\circ\)
a. \(100^\circ\) b. \(110^\circ\) c. \(120^\circ\) d. \(130^\circ\)

2. a. \(70^\circ\) b. \(80^\circ\) c. \(90^\circ\) d. \(100^\circ\)
a. \(110^\circ\) b. \(120^\circ\) c. \(130^\circ\) d. \(140^\circ\)

3. a. \(95^\circ\) b. \(105^\circ\) c. \(110^\circ\) d. \(115^\circ\)
a. \(35^\circ\) b. \(40^\circ\) c. \(45^\circ\) d. \(50^\circ\)

4. a. \(30^\circ\) b. \(35^\circ\) c. \(40^\circ\) d. \(45^\circ\)
a. \(55^\circ\) b. \(60^\circ\) c. \(65^\circ\) d. \(70^\circ\)

5. a. 9 b. 7 c. 12 d. 14
a. 20 b. 17 c. 15 d. 22

6. a. 2 b. 3 c. 4 d. 5
a. 16 b. 18 c. 20 d. 24

7. a. 2 b. 3 c. 4 d. 5
a. 9 b. 11 c. 13 d. 15

8. a. \(110^\circ\) b. \(120^\circ\) c. \(130^\circ\) d. \(140^\circ\)
a. \(40^\circ\) b. \(50^\circ\) c. \(60^\circ\) d. \(70^\circ\)

9. a. 16 cm b. 20 cm c. 24 cm d. 30 cm

10. a. 12 cm b. 15 cm c. 18 cm d. 20 cm
a. 17 cm b. 20 cm c. 22 cm d. 25 cm

11. a. 20 inches b. 25 inches c. 28 inches d. 32 inches
a. 10 inches b. 12 inches c. 15 inches d. 18 inches

12. a. 4 b. 5 c. 6 d. 7
a. 8 b. 10 c. 12 d. 14
a. 10 b. 12 c. 14 d. 16
a. 12 b. 15 c. 18 d. 20

Answer :

1. Always true: A square meets the criteria of a rectangle.

2. Never true: A rhombus is not always a square.

3. Never true: A parallelogram is not always a square.

4. Never true: A rectangle is not always a rhombus.

5. Sometimes true: If a parallelogram meets certain criteria, it can be a square.

6. Never true: A parallelogram is not always a rectangle.

7. Sometimes true: If a quadrilateral has certain properties, it can be a parallelogram.

8. Always true: A square meets the definitions of both a rectangle and a rhombus.

9. Always true: An equilateral quadrilateral is a special case of a rhombus.

10. Never true: An equiangular quadrilateral does not necessarily have right angles like a rectangle.

Let's analyze each statement:

1. A square is a rectangle: Always true. By definition, a square is a quadrilateral with four right angles and equal sides. A rectangle is a quadrilateral with four right angles. Since all squares meet the definition of a rectangle, this statement is always true.

2. A rhombus is a square: Never true. A square is a special case of a rhombus where all angles are right angles. However, a rhombus is a quadrilateral with all sides of equal length, but not necessarily right angles.

3. A parallelogram is a square: Never true. A square is a special case of a parallelogram where all angles are right angles and adjacent sides are equal. However, not all parallelograms meet these criteria.

4. A rectangle is a rhombus: Never true. A rhombus has all sides of equal length, while a rectangle has opposite sides of equal length and all right angles.

5. A parallelogram is a square: Sometimes true. A square is a special case of a parallelogram where all angles are right angles and adjacent sides are equal. If a parallelogram meets these criteria, it is a square.

6. A parallelogram is a rectangle: Never true. A rectangle is a special case of a parallelogram where all angles are right angles. However, not all parallelograms meet this criterion.

7. A quadrilateral is a parallelogram: Sometimes true. A parallelogram is a quadrilateral where opposite sides are parallel. If a quadrilateral has opposite sides that are parallel, it is a parallelogram.

8. A square is a rectangle and a rhombus: Always true. By definition, a square is both a rectangle (all right angles) and a rhombus (all sides equal).

9. An equilateral quadrilateral is a rhombus: Always true. An equilateral quadrilateral has all sides of equal length, which meets the definition of a rhombus.

10. An equiangular quadrilateral is a rectangle: Never true. A rectangle has four right angles, while an equiangular quadrilateral may have four equal angles, but not necessarily right angles.

Summary: Each statement was analyzed based on the definitions of the shapes involved, determining whether the statement holds true in all cases, some cases, or no cases.

The question probable maybe:

Answer the following statements with always true, sometimes true, or never true and explain why.

1. a square is a rectangle

2. a rhombus is a square

3. a parallelogram is a square

4. a rectangle is a rhombus

5. a parallelogram is a square

6. a parallelogram is a rectangle

7. a quadrilateral is a parallelogram

8. a square is a rectangle and a rhombus

9. an equilateral quadrilateral is a rhombus

10. an equiangular quadrilateral is a rectangle

Thanks for taking the time to read Part A Answer the following statements with Always True Sometimes True or Never True 1 A square is a rectangle 2 A rhombus is a. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada