Understanding Properties of Parallelograms
Explore the relationships among sides, angles, diagonals, and transversals of parallelograms through theorems and examples. Discover how opposite sides and angles of a parallelogram are congruent, and solve problems involving consecutive angles and algebraic computations. Practice finding side lengths, angles, and perimeters of parallelograms in various scenarios. Homework assignments included for further practice.
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Presentation Transcript
Section 6 2 Properties of Parallelograms Objectives: To use relationships among sides and among angles of parallelograms To use relationships involving diagonals of parallelograms or transversals
Theorem 6 1 Opposite sides of a parallelogram are congruent
Consecutive Angles: Angles of a polygon that share a side Consecutive angles are supplementary!
Example 1 Using Consecutive Angles Find m S in RSTW. A) If consecutive angles of a quadrilateral are supplementary, must the quadrilateral be a parallelogram?
B) Use KMOQ to find m 0. C) If m BAD = y and m ADC = 4y 70, find y.
Theorem 6 2 Opposite angles of a parallelogram are congruent
Example 2 Using Algebra Find the values of x in PQRS. Then find QR and PS. A)
B) Find the value of y in EFGH. Then find m E, m G, m F, and m H.
Find the value of d in ABCD. Then C) find m A.
Example 3 Parallelograms & Perimeter A) ABCD. The perimeter is 48 inches. AB is 5 inches less than BC. Find the lengths of all four sides of
B) ABCD. The perimeter is 92 cm. AD is 7 cm more than twice AB. Find the lengths of all four sides of
Homework: Textbook Page297 298; #2 16 even, 39 - 41
Warm Up Solve each system of linear equations. 1) 2x = y + 4 x + 2 = y 2) 2x = y + 3 3x = 2y Find the lengths of all four sides of ABCD. The perimeter is 92 cm. AD is 7 cm more than twice AB. 3)
Section 6 2 Continued Objectives: To use relationships involving diagonals of parallelograms or transversals
Theorem 6 3 The diagonals of a parallelogram bisect each other.
Example 3 Using Algebra Find the values of x and y in ABCD. Then find AE, EC, BE, and ED. A)
B) and XZ. Find the values of a and b. Then find WY
Find the values of x and y in PQRS C) when PT = 2x 7, TR = 3y 9, QT = y 1, and TS = 2y 5.
Theorem 6 4 If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Homework: Textbook Page 298 300; # 17 22, 24 32 Even, 44 52 Even
