In angle ABC, AB=BC and in triangle ACD, AD=CD. prove that angle BAD=angle BCD.
Answers
Step-by-step explanation:
In the figure, AB = BC and angles BAD and BCD are right angles. Which one of the following conclusions may be drawn?
(A) The measure of angle BCA = the measure of angle CAD
(B) The measure of angle B is greater than the measure of angle D
(C) AC = CD
(D) AD = CD
(E) BC is shorter than CD
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As there don't seem to be special symmetries (like regular polygons), we'll look for specific Geometric rules.
This is a Precise approach.
Since AB = BC then the base angles of triangle BAC are equal.
This mean that the base angles of triangle DCA must also be equal as they complement those of BAC to 90 degrees.
Therefore, AD = CD, answer (D).
The only other fact that we know about the figure is that angle ABC and angle CDA sum to 180 (because the 4 angles of a quadrilateral sum to 360) but as this does not appear in any of the answer choices it is not helpful.
Answer:
In angle ABC, AB=BC and in triangle ACD, AD=CD. prove that angle BAD=angle BCD