Properties of Parallelograms PDF

PROPERTIES OF PARALLELOGRAM  Objectives At the end of this lesson, the learner should be able to  accurately determine the different properties of parallelograms;  correctly apply the properties of parallelograms in solving for the measure of the sides and angles; and  correctly solve w...

PROPERTIES OF PARALLELOGRAM  Objectives At the end of this lesson, the learner should be able to  accurately determine the different properties of parallelograms;  correctly apply the properties of parallelograms in solving for the measure of the sides and angles; and  correctly solve word problems involving the  Learn about It! 1 Properties of Parallelogram Property 1: A parallelogram must have a pair of parallel opposite sides. AB II CD AC II BD  Learn about It! Property 2: In a parallelogram, any 1 two opposite sides are congruent. AB ≅ CD AC ≅ BD  Learn about It! Property 3: In a parallelogram, any two 1 opposite angles are congruent. ∠A ≅ ∠D ∠C ≅ ∠B  Learn about It! Property 4: In a parallelogram, any two consecutive angles are supplementary. m∠A + m∠B = 180 m∠B + m∠D = 180 m∠D + m∠C = 180  Learn about It! Property 5: The diagonals of a parallelogram bisect each other. Diagonal AD bisects BC then BE ≅ CE E Diagonal BC bisects AD then AE ≅ DE  Learn about It! Property 6: A diagonal of a parallelogram form two congruent triangles. ∠DAB ≅ ∠ADC  Try It! Problem 1: Solve for and the measures of the interior angles of the parallelogram. 12𝑥+4 Solution: S≅ 1 3 𝑥 −6  Try It! Problem 1: Solve for and the measures of the interior angles of the parallelogram. Solution: 12𝑥+4 1 3 𝑥 −6  Try It! Problem 1: Solve for and the measures of the interior angles of the parallelogram. Solution: 12𝑥+4 1 3 𝑥 −6  Try It! Problem 2: In parallelogram , and. Solve for and the measures of the interior angles of the parallelogram.  Try It! Example 1: In parallelogram , and. Solve for and the measures of the interior angles of the parallelogram. Solution: Since these angles are congruent, it follows that their measures are equal. Let us equate their measures, substitute their corresponding expressions, and solve for.  Try It! Example 1: In parallelogram , and. Solve for and the measures of the interior angles of the parallelogram. Solution:  Try It! Example 1: In parallelogram , and. Solve for and the measures of the interior angles of the parallelogram. Solution: 2. Substitute the value of to solve for and. Since , we can expect that their measures would be equal.  Try It! Example 1: In parallelogram , and. Solve for and the measures of the interior angles of the parallelogram. Solution:  Try It! Example 1: In parallelogram , and. Solve for and the measures of the interior angles of the parallelogram. Solution:  Try It! Problem 3: In parallelogram FIND, solve for the value of x. F I Solution: 19 19x FN = ID 19 = 19x 1 = x or x = 1 N D  Try It! Problem 4: In parallelogram FIND, solve for the value of x. S A Solution: AD = SN 14 3x - 1 3x -1 = 14 3x = 1+14 3x = 15 N D x=5  Try It! Problem 5: is a parallelogram whose diagonals meet at. If units and units, solve for the measures of , , and. Solution: 1. Draw the figure and indicate the measurements.  Try It! Example 2: is a parallelogram whose diagonals meet at. If units and units, solve for the measures of , , and. Solution: 2. Identify the property of parallelogram that must be used to solve for. We can solve for by utilizing Property 5 of a parallelogram. It states that diagonals of a parallelogram bisect each other.  Try It! Example 2: is a parallelogram whose diagonals meet at. If units and units, solve for the measures of , , and. Solution: Thus, in the given parallelogram, we can conclude that and. Since these segments are congruent, then it follows that their measures are equal. We can use this to solve for.  Try It! Example 2: is a parallelogram whose diagonals meet at. If units and units, solve for the measures of , , and. Solution:  Try It! Example 2: is a parallelogram whose diagonals meet at. If units and units, solve for the measures of , , and. Solution: 3. Substitute the value of to solve for the measures of and.  Try It! Example 2: is a parallelogram whose diagonals meet at. If units and units, solve for the measures of , , and. Solution:  Try It! Example 2: is a parallelogram whose diagonals meet at. If units and units, solve for the measures of , , and. Solution: We have verified that and are congruent. Therefore, units and units.  Try It! Example 2: is a parallelogram whose diagonals meet at. If units and units, solve for the measures of , , and. Solution: 4. Use the measures of and to find the measure of. To get the measure of , add the measures of and.  Try It! Example 2: is a parallelogram whose diagonals meet at. If units and units, solve for the measures of , , and. Solution: Therefore units.  Let’s Practice! Individual Practice: 1. is a parallelogram. If and , solve for , , , and. 2. The perimeter of parallelogram is units. If units and units, solve for.  Let’s Practice! Group Practice: To be done in groups of five. The shape of a certain lot is a parallelogram. Marco and Carmen walked towards the diagonal pathway. They walk halfway at -m and -m mark, respectively, and meet at a right angle. What is the area of the lot? Key Points Properties of Parallelogram 1 Property 1: A parallelogram must have a pair of parallel opposite sides. Property 2: In a parallelogram, any two opposite sides are congruent Property 3: In a parallelogram, any two opposite angles are congruent. Property 4: In a parallelogram, any two consecutive angles are supplementary. Property 5: The diagonals of a parallelogram bisect each other. Property 6: A diagonal of a parallelogram form two congruent triangles.