Lesson 5 9 Show that a quadrilateral is
- Slides: 10
Lesson 5. 9 Show that a quadrilateral is a parallelogram. Page 311
Which of these are not parallelograms? B A F G C H A parallelogram is a quadrilateral with both pairs of opposite sides parallel. D I
Properties of parallelograms
Example 1 a Explain how you know that the quadrilateral QRST is a parallelogram. Q By Theorem 5. 23 we know that if both pairs of opposite sides are congruent then the quadrilateral is a parallelogram. Since this is a convex quadrilateral we know that the angle sum will be 360°.
Example 1 b Explain how you know that the quadrilateral QRST is a parallelogram. Q Since QP = PS we know that P bisects the QS diagonal. Since TP = PR we know that P bisects the TR diagonal. By Theorem 5. 25 we know that the quadrilateral is a parallelogram because the diagonals bisect each other.
Example 2 for what values of x is the figure a parallelogram? Since the sides are parallel by the drawing we only have to find what values of x will make the two expressions equal.
Homework 5. 9 page 313 • 1 – 11 odd
#1 What theorem can you use to show that the quadrilateral is a parallelogram? X
#3. What theorem can you use to show that the quadrilateral is a parallelogram? Since 5 = 5 and 3. 6 = 3. 6 we know that the diagonals bisect each other.
For what values of x is the figure a parallelogram?
