"Question 8 ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D.
Class 9 - Math - Quadrilaterals Page 146"
Answers
Rectangle: a quadrilateral in opposite sides are parallel and equal and one angle is 90° is called a rectangle.
Square: a quadrilateral in
which all four sides are equal , both pairs of opposite sides are parallel and
one angle is a right angle is called a square
In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i e, corresponding parts of Congruent Triangles.
ASA(angle side angle):
Two Triangles are congruent if two angles and the included side of One triangle are equal to two angles & the included side of the other triangle.
SSS(side side side):
Three sides of One triangle are equal to the three sides of another triangle then the two Triangles are congruent.
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solution is in the attachment,....
Given;- -ABCD is a rectangle in which diagonal AC bisects angle A as well as angle C .
To prove :-1) ABCD is a square .
2)diagonal BD bisects angle B as well as angle d .
PROOF:-1)Since AC bisects angle A as well as angle C in the rectangle ABCD .
angle 1=angle 2 =angle 3 =angle 4 (each =90/2=45 degree)
In triangle ,angle 2 = angle 4
=AD=CD ( Sides opposite to equal angles)
Thus, the rectangle ABCD is a square .
2)In a square ,diagonals bisect the angles .
So, BD bisects angle B as well as angle D .
Hope helps!!
