Let us prove this property considering the following given fact and using the same figure. The consecutive angles of a parallelogram are supplementary. Consecutive Angles of a Parallelogram are Supplementary This shows that the consecutive angles are supplementary. = 2(∠A + ∠B) = 360º (We can substitute ∠C with ∠A and ∠D with ∠B since it is given that ∠A =∠C and ∠B =∠D) The sum of all the four angles of this quadrilateral is equal to 360°. Given: ∠A =∠C and ∠B=∠D in the quadrilateral ABCD. The converse of the above theorem says if the opposite angles of a quadrilateral are equal, then it is a parallelogram. Hence proved, that opposite angles in any parallelogram are equal. This gives ∠B = ∠D by CPCT (corresponding parts of congruent triangles). Thus, the two triangles are congruent, △ABC ≅ △ADC Proof: In the parallelogram ABCD, diagonal AC is dividing the parallelogram into two triangles. Given: ABCD is a parallelogram, with four angles ∠A, ∠B, ∠C, ∠D respectively. Theorem: In a parallelogram, the opposite angles are equal. Opposite Angles of a Parallelogram are Equal Let us learn about these two special theorems of a parallelogram in detail. Consecutive angles of a parallelogram are supplementary.The opposite angles of a parallelogram are equal.Two of the important theorems are given below: The theorems related to the angles of a parallelogram are helpful to solve the problems related to a parallelogram. State the properties you use to find them.Theorems Related to Angles of a Parallelogram The adjacent figure HOPE is a parallelogram.Find the measure of each of the angles of the parallelogram. Two adjacent angles of a parallelogram have equal measure.The measures of two adjacent angles of a parallelogram are in the ratio 3:2.Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.Let's look into a quadrilateral ABCD and check if it is a parallelogram using the following conditions: (i) For, ∠D + ∠B = 180°, ABCD may or may not be a parallelogram (ii) For, AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm, ABCD cannot be a parallelogram (iii) For, ∠A = 70° and ∠C = 65°, ABCD cannot be a parallelogram. NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.3 Question 3 Video Solution: Can a quadrilateral ABCD be a parallelogram if (i) ∠D + ∠B = 180°? (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii) ∠A = 70° and ∠C = 65°? ☛ Check: NCERT Solutions for Class 8 Maths Chapter 3 (iii) Property of a parallelogram: In a parallelogram opposite angles are equal. Opposite sides AD and BC are of different lengths. (ii) Property of parallelogram: The opposite sides of a parallelogram are of equal length. Hence, using the given condition ∠D + ∠B = 180° we can say that yes, it may or may not be a parallelogram. The sum of the measures of the adjacent angles should be 180° and opposite angles should also be of the same measure. If the following conditions are fulfilled, then ABCD is a parallelogram. ∠A + ∠C = 180° (Opposite angles should also be of same measures.) (i) Using the angle sum property of a quadrilateral, (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? Can a quadrilateral ABCD be a parallelogram if
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