a.
To find: If the given quadrilateral is a special quadrilateral and if then to write the proof.
a.
Answer to Problem 40WE
Yes, the given quadrilateral is a trapezoid
Explanation of Solution
Given:
A quadrilateral with two sides parallel and one diagonal bisects only one angle.
Proof:
A trapezoid is a quadrilateral with only one pair of parallel sides and the other pair of non-parallel sides.
In a trapezium two pairs of adjacent
Now in quadrilateral
So,
Therefore by (i) and (ii),
Quadrilateral
Conclusion:
Therefore, quadrilateral
b.
To find: if the given quadrilateral is a special quadrilateral and if then to write the proof.
b.
Answer to Problem 40WE
Yes, the given quadrilateral is a regular trapezoid
Explanation of Solution
Given:
Quadrilateral with two sides parallel and one diagonal bisects two angles of the quadrilateral.
Proof:
Since
So,
And
Since
So,
And
Now since
So,
From (ii), (iv), and (v),
Now in
Therefore by (vi) and (vii),
The quadrilateral
Conclusion:
Therefore, the quadrilateral
Chapter 5 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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- 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