1 / 21

Warm Up:

Warm Up:. Solve for x and y in the following parallelogram. What properties of parallelograms did you use when solving? What is the measure of CD? What is the measure of Angle C? What is the sum of the interior angles of a dodecagon?. 1. B. C. (16x – 4) o. 5y – 1 . 2y + 8.

orsen
Download Presentation

Warm Up:

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm Up: • Solve for x and y in the following parallelogram. What properties of parallelograms did you use when solving? • What is the measure of CD? • What is the measure of Angle C? • What is the sum of the interior angles of a dodecagon? 1. B C (16x – 4)o 5y – 1 2y + 8 (14x + 34)o A D 2. 3. 4.

  2. Conditions of Parallelograms (6.3) and Special Parallelograms (6.4) • IF a quadrilateral is a parallelogram, THEN its opposite sides are congruent.

  3. Conditions of Parallelograms (6.3) and Special Parallelograms (6.4) • IF a quadrilateral is a parallelogram, THEN its opposite sides are congruent. • IF both pairs of opposite sides of a quadrilateral are congruent, THEN the quadrilateral is a parallelogram.

  4. Conditions of Parallelograms (6.3) and Special Parallelograms (6.4) • IF a quadrilateral is a parallelogram, THEN its opposite angles are congruent.

  5. Conditions of Parallelograms (6.3) and Special Parallelograms (6.4) • IF a quadrilateral is a parallelogram, THEN its opposite angles are congruent. • IF both pairs of opposite angles of a quadrilateral are congruent, THEN the quadrilateral is a parallelogram.

  6. Conditions of Parallelograms (6.3) and Special Parallelograms (6.4) • IF a quadrilateral is a parallelogram, THEN its consecutive angles are supplementary. B C xo (180 – x)o (180 – x)o xo A D

  7. Conditions of Parallelograms (6.3) and Special Parallelograms (6.4) • IF a quadrilateral is a parallelogram, THEN its consecutive angles are supplementary. • IF an angle of a quadrilateral is supplementary to both of its consecutive angles, THEN the quadrilateral is a parallelogram. B C xo (180 – x)o (180 – x)o xo A D

  8. Conditions of Parallelograms (6.3) and Special Parallelograms (6.4) • IF a quadrilateral is a parallelogram, THEN its diagonals bisect each other.

  9. Conditions of Parallelograms (6.3) and Special Parallelograms (6.4) • IF a quadrilateral is a parallelogram, THEN its diagonals bisect each other. • IF the diagonals of a quadrilateral bisect each other, THEN the quadrilateral is a parallelogram.

  10. Conditions of Parallelograms (6.3) and Special Parallelograms (6.4) • IF one pair of opposite sides of a quadrilateral are parallel AND congruent, THEN the quadrilateral is a parallelogram.

  11. Show that ABCD is a parallelogram for m = 12 and n = 9.5; which one of the conditions of parallelograms did you use? B C (7m – 29)o (12n + 11)o (2m + 31)o A D

  12. Are each of the given quadrilaterals also parallelograms? Justify your answer. # 1 # 2 # 3 7 7

  13. Find x and y so the quadrilateral is a parallelogram. (x – 12)o B C (3y – 4)o (4x – 8)o A D (1/2 y)o

  14. RECTANGLES

  15. RECTANGLE • Four Right Angles • Congruent Diagonals • Properties of a Parallelogram

  16. RHOMBUSES

  17. RHOMBUS • Four Congruent Sides • Perpendicular Diagonals • Diagonals Bisect Opposite • Angles • Properties of a Parallelogram

  18. SQUARES

  19. SQUARE • Properties of a Rectangle • Properties of a Rhombus

  20. ABCD is a rhombus. Find the measure of Angle B. (y + 2)o B C (2y + 10)o A D

  21. Show the diagonals • ofsquare ABCD • are congruent • perpendicular • bisectors of each • other. • A (-1, 0) • B (-3, 5) • C (2, 7) • D (4, 2)

More Related