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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.

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.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter5: Similar Triangles
Section5.3: Proving Triangles Similar
Problem 3E: Classify as true or false: a If the vertex angles of two isosceles triangles are congruent, the...
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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.
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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