Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Question
26
A
D
a В
2 Euclid's approach to geometry
В
B
a
C
Figure 2.5: Dividing a parallelogram into triangles
Therefore, the triangles are congruent by ASA, and in particular we
have the equalities |AB| = |DC| and |AD| = |BC| between corresponding
sides. But these are also the opposite sides of the parallelogram.
Exercises
Using the parallelogram side theorem and ASA, find congruent triangles in
Figure 2.6. Hence, show that the diagonals of a parallelogram bisect each
other.
Figure 2.6: A parallelogram and its diagonals
Deduce that the diagonals of a rhombus-a parallelogram whose sides are
all equal-meet at right angles. (Hint: You may find it convenient to
use SSS, which says that triangles are congruent when their correspond-
ing sides are equal.)
Prove the isosceles triangle theorem differently by bisecting the angle at A.
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Transcribed Image Text:26 A D a В 2 Euclid's approach to geometry В B a C Figure 2.5: Dividing a parallelogram into triangles Therefore, the triangles are congruent by ASA, and in particular we have the equalities |AB| = |DC| and |AD| = |BC| between corresponding sides. But these are also the opposite sides of the parallelogram. Exercises Using the parallelogram side theorem and ASA, find congruent triangles in Figure 2.6. Hence, show that the diagonals of a parallelogram bisect each other. Figure 2.6: A parallelogram and its diagonals Deduce that the diagonals of a rhombus-a parallelogram whose sides are all equal-meet at right angles. (Hint: You may find it convenient to use SSS, which says that triangles are congruent when their correspond- ing sides are equal.) Prove the isosceles triangle theorem differently by bisecting the angle at A.
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