Transcription of Geometry Worksheet Quadrilaterals
1 Geometry Worksheet Quadrilaterals Section: Name: Mr. Lin 1 Do Now: Write the definition of Quadrilaterals : _____. Parts & Properties of the Quadrilaterals 1. _____: Vertices that are endpoints of the same side. Example: _____. 2. _____: Sides that have a common endpoint. Example: _____. 3. _____: Sides that do not have a common endpoint. Example: _____. 4. _____: Angles whose vertices are consecutive. Example: _____. 5. _____: Angles whose vertices are not consecutive. Example: _____.
2 6. _____: A line segment whose endpoints are two nonadjacent vertices of the quadrilateral. Example: _____. 7. The sum of the measures of the angles of a quadrilateral is: _____. Example: _____. Parallelograms 8. Write the definition of parallelogram: _____ _____. 9. The notation of parallelogram: _____. Name the parallelogram and show its parallel sides: _____ _____. Theorems of Parallelogram 10. Theorem of Dividing Diagonals A diagonal divides a parallelogram into two congruent triangles Given: ABCD is a parallelogram Prove: ABD CDB Proof: _____.
3 11. Theorem of Opposite Sides Opposite sides of a parallelogram are congruent Given: ABCD is a parallelogram Prove: BC DA Proof: _____. R P S Q C A D B Geometry Worksheet Quadrilaterals Section: Name: Mr. Lin 2 DoNow: ABCD is a parallelogram, what s the perimeter of ABCD ? 12. Theorem of Opposite Angles Opposite angles of a parallelogram are congruent A C, and B D Given: ABCD is a parallelogram Prove: A C, and B D Proof: _____ 13.
4 ABCD is a parallelogram, what are the values of x and y? 14. Theorem of Bisecting Diagonals The diagonals of a parallelogram bisect each other Given: ABCD is a parallelogram Prove: AC and BD bisect each other at O Proof: _____ 15. ABCD is a parallelogram, ABCD is a parallelogram, if AO = 3, BO = 4 AB = 6, AC + BD = ? 16. ABCD is a parallelogram, if AO = x+4, BO = 2y-6, CO = 3x-4, an DO = y+2, solve for x and y. 17. Theorem of Consecutive Angles The consecutive angles of a parallelogram are supplementary Given: ABCD is a parallelogram Prove: A and B are supplementary C and D are supplementary A and D are supplementary B and C are supplementary Proof: _____ 18.
5 ABCD is a parallelogram, what are the values of x, y and z? C A D B x + 7 3x - 3 y + 2 2y 6 C A D B x + 20o 2x 60 o 180 o y y 20 o C A D B 6 4 3 O C A D B y+2 2y 6 x+4 O 3x 4 C A D B 120o y o z o x o Geometry Worksheet Quadrilaterals Section: Name: Mr. Lin 3 19. ABCD is a parallelogram, what are the values of x and y? 20. ABCD is a parallelogram, calculate the perimeter of ABCD? 21. ABCD is a parallelogram, solve for x. 22.
6 Given: ABCD is a parallelogram Prove: XO YO 23. Given: ABCD is a parallelogram, BO OD Prove: EO OF 24. Given: ABCD is a parallelogram, AF || CE Prove: FAB ECD Review: Theorems of Parallelogram _____ _____ _____ _____ _____ C A D B x+30o y +20o x 30 o C A D B x + 30 2x 10 2y 10 y + 10 C A D B x+10 2x x+30 O x 10 C A D B X O Y C A D B E O F C A D B E F Geometry Worksheet Quadrilaterals Section: Name: Mr.
7 Lin 4 Prove Quadrilaterals are Parallelograms 25. List the criteria for proving Quadrilaterals are parallelograms: (A) _____ (B) _____ (C) _____ (D) _____ (E) _____ (F) _____ 26. Parallel Opposite Sides If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram Given: If AB || CD, and BC || DA Prove: ABCD is a parallelogram Proof: _____ 27. Application Example If m 1 = m 2 = m 3, then ABCD is a parallelogram 28.
8 Application Example ABCD is a quadrilateral as shown below, solve for x 29. Congruent Opposite Sides If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram Given: If AB CD, and BC DA Prove: ABCD is a parallelogram Proof: _____ 30. Application Example ABCD is a quadrilateral as shown below, solve for x 31. Application Example ABCD is a parallelogram, if DF = BE, then AECF is also a parallelogram 2 3 1 C A D B 50o 3x 20 50o 60o 60o 2x + 10 5 2x 30 5 6 6 x + 50 C A D B E F Geometry Worksheet Quadrilaterals Section: Name: Mr.
9 Lin 5 32. Congruent & Parallel Opposite Sides If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram Given: If AB || CD, and AB CD Prove: ABCD is a parallelogram Proof: _____ 33. Application Example ABCD is a quadrilateral as shown below, solve for x and y. 34. Application Example ABCD is a parallelogram, if m 1 = m 2, then AECF is also a parallelogram 35. Congruent Opposite Angles If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Given: A C, and B D Prove: ABCD is a parallelogram Proof: _____ 36.
10 Application Example ABCD is a quadrilateral, solve for x 37. Application Example If m 1 = m 2 = m 3, then ABCD is a parallelogram. 30o y + 50 10 10 30o x + 5 2y 20 C A D B E F 2 1 130o 50o 50o x + 30 130o 2x 40 5 2 3 1 C A D B 4 Geometry Worksheet Quadrilaterals Section: Name: Mr. Lin 6 38. Bisecting Diagonals If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram Given: AC and BD bisect each other at O Prove: ABCD is a parallelogram Proof: _____ 39.
