To prove: The given theorem.
Explanation of Solution
Given information:
The theorem: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
The diagram:
Formula used:
The opposite
The sides of a rhombus are congruent.
SAS congruence:
If two pairs of corresponding sides and one pair of corresponding angles of two
In the triangles JKL and JML;
Thus, the triangles JKL and JML are congruent.
Similarly, the triangles KLM and KJM are also congruent.
Since, the triangles are congruent;
So,
It is known that all sides of a rhombus are congruent.
Thus, the parallelogram JKLM is a rhombus.
Hence, the theorem is proved.
Chapter 6 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Thinking Mathematically (6th Edition)
Calculus and Its Applications (11th Edition)
Calculus: Early Transcendentals (2nd Edition)
College Algebra
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
- 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