
To prove:
Given:
The diagram:
Concept Used:
Postulate 11: corresponding
Theorem 3-5: Alternate interior angles between parallel lines must be equal.
Theorem 5-1: Opposite sides of a parallelogram are congruent.
Explanation:
Consider the figure shown below:
It is known that a parallelogram is a quadrilateral whose both pairs of opposite sides are parallel.
From the above figure, it can be observed that the angles
It is given that,
Thus, by the postulate 11, it can be said that the lines
Similarly, the angles
It is given that,
Thus, by the theorem 3-5, it can be said that the lines
That is, for the quadrilateral
So, it can be said that
Now by theorem 5-1, it is known that opposite sides of a parallelogram are congruent. So,
Chapter 9 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
A First Course in Probability (10th Edition)
Elementary Statistics
Elementary Statistics: Picturing the World (7th Edition)
Introductory Statistics
University Calculus: Early Transcendentals (4th Edition)
- 39 Two sides of one triangle are congruent to two sides of a second triangle, and the included angles are supplementary. The area of one triangle is 41. Can the area of the second triangle be found?arrow_forwardA parallelogram with an area of 211.41 m^2 hast a base Thatcher measures 24.3m. Find ist height.arrow_forwardBH is tangent to circle A and DF is a diameter. I don't know where to go from here. May you help please?arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning

