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The figure shows rhombus ABCD. Which of the following conditions satisfies the criteria for rhombi?

- Parallelogram rhombus ABCD with diagonals BD and AC intersecting at E
- m∠BAE = 90°
- m∠BAE = 45°
- m∠BEC = 90°
- m∠BEA = 45°

Question 4 (Multiple Choice, Worth 1 point) (02.06 MC)

ABCD is a parallelogram with diagonal AC. If the measure of angle CAB is 24° and the measure of angle ADC is 127°, what is the measure of angle DAC?

- Parallelogram ABCD with diagonal AC; the measure of angle ADC is 127 degrees, and the measure of angle CAB is 24 degrees.
- 29°
- 48°
- 79°
- 103°

Question 5 (Multiple Choice, Worth 1 point) (02.06 MC)

In parallelogram EFGH, the measure of angle E is (2x + 3)° and the measure of angle F is (3x − 33)°. What is the measure of angle E?

- 36°
- 42°
- 87°
- 93°

Question 6 (Multiple Choice, Worth 1 point) (02.06 MC)

The diagonals of parallelogram LMNO intersect at point P. If MP = 2x − 1 and OP = 3x − 4, what is MP?

- −1
- 1
- 3
- 5

Question 7 (Multiple Choice, Worth 1 point) (02.06 MC)

Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG. The measure of angle HGF is (5y − 2)°, and the measure of angle EFG is (4y + 4)°. What is the measure of angle HGF?

- Trapezoid E F G H is drawn with parallel bases E H and F G.
- 20°
- 28°
- 78°
- 90°

Question 8 (Multiple Choice, Worth 1 point) (02.06 MC)

Isosceles trapezoid ABCD is shown with midsegment EF. If base BC = 15x, base AD = 32x − 2, and EF = 20.5x + 8, what is BC?

- Isosceles trapezoid A B C D is drawn with parallel bases A D and B C and midsegment E F.
- 45
- 55
- 60
- 82

Question 9 (Multiple Choice, Worth 1 point) (02.06 LC)

In parallelogram DEFG, the measure of angle D = 62°. What is the measure of angle E?

- 28°
- 62°
- 90°
- 118°

Question 10 (Multiple Choice, Worth 1 point) (02.06 MC)

The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:

Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD. According to the given information, segment AB ...

Answer :

The condition that satisfies the criteria for rhombi would be = m∠BEC = 90° . That is option C.

What are the properties of the rhombus?

The properties of a rhombus include the following:

  • All sides are equal in length.

  • Opposite angles are equal in a rhombus.

  • The diagonals bisect each other at 90 degrees.

  • Adjacent angles add up to 180 degrees.

Therefore, the condition that satisfies the criteria for rhombi would be = m∠BEC = 90° because the diagonals of a rhombi bisect each other at 90 degrees.

Complete question:

Question 3: The figure shows rhombus ABCD. Which of the following conditions satisfies the criteria for rhombi? Parallelogram rhombus ABCD with diagonals BD and AC intersecting at E

a.) m∠BAE = 90°

b.) m∠BAE = 45°

c.) m∠BEC = 90°

d.) m∠BEA = 45°

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