Introduction

Parallelograms are a sort of quadrilateral which have distinctive properties. Figuring out these properties can assist you remedy issues and perceive geometric ideas. On this article, we are going to undergo some apply issues associated to the properties of parallelograms and supply a solution key.

Properties of Parallelograms

Earlier than we dive into the apply issues, let’s overview the properties of parallelograms. Parallelograms have two pairs of parallel sides and reverse angles which can be congruent. Moreover, the alternative sides of a parallelogram are congruent in size and the diagonals bisect one another.

Follow Drawback 1

Discover the worth of x within the parallelogram under: To resolve this drawback, we will use the truth that reverse sides of a parallelogram are congruent. We will arrange an equation: 2x + 7 = 3x – 1 Fixing for x, we get: x = 8

Follow Drawback 2

Discover the measure of angle x within the parallelogram under: To resolve this drawback, we will use the truth that reverse angles of a parallelogram are congruent. We will arrange an equation: 3x – 5 = 5x – 35 Fixing for x, we get: x = 15 Due to this fact, angle x measures 3(15) – 5 = 40 levels.

Follow Drawback 3

Discover the worth of x within the parallelogram under: To resolve this drawback, we will use the truth that diagonals of a parallelogram bisect one another. We will arrange an equation: 4x – 6 = 2x + 18 Fixing for x, we get: x = 12 Due to this fact, the worth of x is 12.

Reply Key

Follow Drawback 1: x = 8 Follow Drawback 2: x = 15, angle x measures 40 levels Follow Drawback 3: x = 12

Conclusion

Figuring out the properties of parallelograms can assist you remedy issues and perceive geometric ideas. By practising issues like those on this article, you possibly can solidify your understanding of those properties.