SOLUTION: in rectangle abcd, diagonals bd and ac are drawn. prove angle dba is congruent to angle cab.

Question 1071182: in rectangle abcd, diagonals bd and ac are drawn. prove angle dba is congruent to angle cab.
Answer by ikleyn(52873) (Show Source): You can put this solution on YOUR website!
.
in rectangle abcd, diagonals bd and ac are drawn. prove angle dba is congruent to angle cab.
~~~~~~~~~~~~~~~~~~~~~

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".

RELATED QUESTIONS
The diagonals of a rectangle are congruent Theorem 4.5.9 Given:Rectangle ABCD with... (answered by solver91311)

In rectangle ABCD, AC and BD are diagonals. if m angle 1 = 55, find m angle... (answered by richard1234)

In ABCD, line segments AC and BD divide each other in half at E. Prove that angle DBC is... (answered by ikleyn)

given trapezoid abcd with diagonals ac and bd intercept at point e prove triangle dec is... (answered by solver91311)

QUESTION: Prove that the area of a kite is equal to half the product of its diagonals. (answered by Edwin McCravy)

I do not understand proofs or in what order to put the statements according to the... (answered by mananth)

Sketch two noncongruent parallelograms ABCD and EFGH such that line AC is congruent to... (answered by solver91311,katewalk11740,ikleyn)

Given: Quadrilateral ABCD with segment AB congruent to segment CD, segment AD congruent... (answered by lynnlo)