Question 1071182: in rectangle abcd, diagonals bd and ac are drawn. prove angle dba is congruent to angle cab.
Answer by ikleyn(52864)   (Show Source):
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in rectangle abcd, diagonals bd and ac are drawn. prove angle dba is congruent to angle cab.
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Consider two triangles, ABC and ABD.
They have common side AB.
They have congruent sides BC and AD (since these sides are the opposite sides of the rectangle.
Also, the triangles have the congruent angles ABC and BAD (they both are right angles).
Hence, the triangles ABC and ABD are congruent in accordance with SAS-test.
Therefore, the corresponding angles of these triangles, the angles DBA and CAB, are congruent.
It is what had to be proved.
Proved and solved.
On congruence tests for triangles see the lesson
- Congruence tests for triangles
in this site.
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lesson is the part if this textbook under the topic "Properties of triangles".
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